Theories of Pashtun origin

There are multiple claims or theories about the origins of the Pashtun tribes, who are classified as an ethnic group based out of Central Asia.
Among them are:
Prior to DNA studies, it was generally acknowledged that their origins were obscure, and modern scholars suggest that a single origin of the Pashtuns is unlikely because they are a tribal confederation.
Bani Israel theory.
There is a tradition among the Pashtuns of being descended from the exiled lost tribes of Israel. This tradition was referenced in 19th-century Western scholarship and was also incorporated in the "Lost Tribes" literature popular at the time (notably George Moore's "The Lost Tribes" of 1861).
Recently (2000s), interest in the topic has been revived by Jerusalem anthropologist Shalva Weil, who was quoted in the popular press to the effect that "Taliban may be descended from Jews".
The traditions surrounding the Pashtuns being remote descendants of the "Lost Tribes of Israel" is to be distinguished from the historical presence of the Jewish community in eastern Afghanistan which flourished from about the 7th century to the early 20th century, but has essentially disappeared due to its emigration to Israel since the 1950s.
Mughal-era historiography.
According to the "Encyclopaedia of Islam", the theory of Pashtun descent from Israelites is traced to "Maghzan-e-Afghani", a history compiled for Khan-e-Jehan Lodhi in the reign of Mughal Emperor Jehangir in the 16th century. The "Maghzan-e-Afghani"'s Bani Israel theory has been discounted by modern authorities, due to numerous historical and linguistic inconsistencies.
In his universal history "Mirat-ul-Alam" – "The Mirror of the World" – Bukhtawar Khan describes the journeys of the Pashtuns from the Holy Land to Ghor, Ghazni, and Kabul. Similarly, Rahmat bin Shah Alam, in his "Khulasat-ul-Ansab" and Fareed-ud-Din Ahmad in "Risala-i-Ansab-i-Afghana" provide the history of the Afghans and deal with their genealogies.
Two of the most famous historical works on the subject are "Tarikh-i-Afghana" – "History of the Afghans" – by Nimat Allah al-Harawi, which was translated by Bernard Dorn in 1829, and "Tarikh-i-Hafiz Rahmatkhani", by Muhammad Zadeek which he wrote in 1770. "Tawarikh-e-Hafiz Rehmat khani"was later translated and provided with footnotes by Khan Roshan khan. These books deal with the early history of the Pashtuns, their origin and wanderings in general. They particularly discuss the Yusefzai (literally "sons of Joseph") and their occupation of Kabul, Bajoor, Swat, Peshawar and some of Charsadda (District of Peshawar).
In his "Travels into Bokhara", which he published in 1835, Sir Alexander Burnes wrote: "The Afghans call themselves Bani Israel, or the children of Israel, but consider the term Yahoodi, or Jew, to be one of reproach. They say that Nebuchadnezzar, after the overthrow of Israel, transplanted them into the towns of Ghore near Bamean and that they were called after their Chief Afghan they say that they lived as Israelites till Khalid summoned them in the first century of the Muhammadans. Having precisely stated the traditions and history of the Afghans I see no good reason for discrediting them… the Afghans look like Jews and the younger brother marries the widow of the elder. The Afghans entertain strong prejudices against the Jewish nation, which would at least show that they have no desire to claim – without just cause – a descent from them." (Sir Alexander Burnes, "Travels into Bokhara", Vol. 2:139-141.)
Burnes was again in 1837 sent as the first British Envoy to the Court of Kabul. For some time he was the guest of King Dost Mohammad Khan. He questioned the King about the descent of the Pashtuns from the Israelites. The King replied that "his people had no doubt of that, though they repudiated the idea of being Jews".
William Moorcroft traveled during 1819 to 1825 through various countries adjoining India, including Afghanistan. "The Khaibarees," he says, "are tall and have a singularly Jewish cast of features." (Moorcroft, "Travels in Himalayan Provinces of Hindustan and the Punjab; in Ladakh and Kashmir, in Peshawar, Kabul, Kunduz and Bokhara", 12)
In his book, "An Historical and Descriptive Account of Persia and Afghanistan", which he published in 1843, J. B. Frazer says: "According to their own tradition they believe themselves to be descendants from the Hebrews… they preserved the purity of their religion until they met with Islam." (J.B. Frazer, "A Historical and Descriptive Account of Persia and Afghanistan", 298)
Sir Henry Yule (1902 "Encyclopædia Britannica", article on Afghanistan) references the tradition:
Thomas Ledlie wrote in an article in the "Calcutta Review" in 1989 that "the Afghans [...] claim themselves to be of Bani Israel." 
Lost Tribes.
It should first be noted that Jewish tradition holds that the tribes were not 'lost', but intermingled. The idea entire tribes - such as the Tribe of Joseph - became separated from the main body is not in accordance with that tradition. It is, however, established historical fact that the early Jewish diaspora was widespread, particularly along the Silk Road, and that sizeable groups migrated, assimilated, and eventually, in some cases, took the local religion. Additionally, the presence of an early Jewish community in the area is well attested, and indeed the community survived to the modern day. It is therefore not unlikely that there is a community descended from early Jewish migrants, but difficult to plausibly call them a 'lost tribe'.
Joseph-Pierre Ferrier wrote his "History of the Afghans" in 1858 (translated by Capt. W. M. Jesse). Ferrier wrote that "When Nadir Shah Afshar marching to the conquest of India arrived at Peshawar, the chief of the tribe of Yoosoof Zyes (Sons of Joseph) presented him with a Bible written in Hebrew and several other articles that had been used in their ancient worship and which they had preserved...This fact, supposing it to be one, if affording evidence sufficiently convincing to some persons, can only be considered as authority with respect to the Yoosoofzyes ; but it does not follow, therefore, that other Afghan tribes are branches from the same stem ; on the contrary, everything leads to the conclusion that, although they all speak a common language, the Pushtoo, the tribes are not all of the same origin - they are distinguished by marked characteristics, moral as well as physical." 
George Moore published his work "The Lost Tribes" in 1861. He argued that these tribes are traceable to India. After giving details of the character of the wandering Israelites, he said: "And we find that the very natural character of Israel reappear in all its life and reality in countries where people call themselves Bani Israel and universally claim to be the descendants of the Lost Tribes. The nomenclature of their tribes and districts, both in ancient Geography, and at the present day, confirms this universal natural tradition. Lastly, we have the route of the Israelites from Media to Afghanistan and India marked by a series of intermediate stations bearing the names of several of the tribes and clearly indicating the stages of their long and arduous journey." [George Moore, "The Lost Tribes"]
Moore goes on to say: "Sir William Jones, Sir John Malcolm and the missing Chamberlain, after full investigation, were of the opinion that the Ten Tribes migrated to India, Tibet, and Cashemire [Kashmir] through Afghanistan." [George Moore, "The Lost Tribes"]
Major H. W. Bellew went on a political mission to Kandahar and published his impressions in his "Journal of a Mission to Kandahar", 1857-8. He then wrote in 1879 his book "Afghanistan and Afghans". In 1880 he was sent, once again on another mission to Kabul, and in the same year he delivered two lectures before the United Services Institute at Simla: "A New Afghan Question", or "Are the Afghans Israelites?" and "Who are the Afghans?" He then published another book: "The Races of Afghanistan". Finally he collected all his facts in "An Enquiry into the Ethnography of Afghanistan", which was published in 1891.
In this work he mentions "Killa Yahoodi" ("Fort of the Jews") (H.W. Bellew, "An Enquiry into the Ethnography of Afghanistan", 34), as being the name of the eastern boundary of their country, and also speaks of "Dasht-i-Yahoodi" ("Jewish plain") (ibid., 4), a place in Mardan District. He concludes: "The Afghan’s accounts of Jacob and Esau, of Moses and the Exodus, of the Wars of the Israelites with the Amalekites and conquest of Palestine, of the Ark of the Covenant and of the election of Saul to the Kingdom, etc., etc., are clearly founded on the Biblical records, and clearly indicate a knowledge of the Old Testament, which if it does not prove the presence of the Christians at least corroborates their assertion that the Afghans were readers of the Pentateuch." (Ibid., 191
The "Lost Tribes" tradition has left some traces in the self-perception of both some Pashtuns and of some Jews well into the 20th century, and until the present day. Thus, Itzhak Ben-Zvi, the second President of Israel, in his 1957 book "The Exiled and the Redeemed", writes that Hebrew migrations into Afghanistan began: "with a sprinkling of exiles from Samaria who had been transplanted there by Shalmaneser, King of Assyria (719 BC) [...] The Afghan tribes, among whom the Jews have lived for generations, are Moslems who retain to this day their amazing tradition about their descent from the Ten Tribes. It is an ancient tradition, and one not without some historical plausibility... if the Afghan tribes persistently adhere to the tradition that they were once Hebrews and in course of time embraced Islam, and there is not an alternative tradition also existent among them, they are certainly Jewish." (p. 176)
In the 2000s, the "lost tribes" hypothesis was popularized by Shalva Weil, an anthropologist at the Hebrew University of Jerusalem,
In 2010, "The Observer" under the title "Pashtun clue to lost tribes of Israel" claimed that 
"Some leading Israeli anthropologists believe that, of all the many groups in the world who claim a connection to the 10 lost tribes, the Pashtuns, or Pathans, have the most compelling case" and on a planned study on the ancestry of the Afridi Pashtuns (while noting that "A previous genetic study in the same area did not provide proof one way or the other"), also citing Weil as saying "Of all the groups, there is more convincing evidence about the Pathans than anybody else, but the Pathans are the ones who would reject Israel most ferociously. That is the sweet irony".
In his book "Abraham's Children", Jon Entine, an American TV News producer and author excludes this possibility.
Greek and Rajput theory.
The British physician and authority on oriental languages, Henry Walter Bellew, accredited for writing the first Pushtu dictionary in colonial India, suggested that the Pashtuns (Pathans) are actually a mixture of the Greek and Rajput peoples.<ref name="The Journal of the Anthropological Institute of Great Britain and Ireland, Vol. 29, No. 1/2 (1899), pp. 2-9">Swatis and Afridis, By T. H. Holdich, "The Journal of the Anthropological Institute of Great Britain and Ireland, Vol. 29, No. 1/2 (1899), pp. 2-9" (retrieved 4 May 2007).</ref> Bellew’s theory was that Pashtun tribal names could be traced to Greek and Rajput names, which posits the further possibility of a great Greek mixing with the ancient border tribes of India. In addition, the renowned Arab historian Masudi wrote that Kandahar, the city in which most Pashtuns were concentrated at the time, "is a country of Rajputs" and was a separate kingdom with a non-Muslim ruler. In the battle between Prithviraj Chauhan and Muhammad of Ghor in 1192 A.D., the historian Firishta stated that "Hindu Afghans were fighting on the side of the Rajput Chief".
Hephthalite (White Hun) descent.
The early ancestors of modern-day Pashtun tribes could possibly be ancient Iranian tribes that spread throughout the eastern Iranian plateau. According to Yu. V. Gankovsky, the Pashtun's probably began as a "union of largely East-Iranian tribes which became the initial ethnic stratum of the Pashtun ethnogenesis, dates from the middle of the first millennium CE and is connected with the dissolution of the Epthalites (White Huns) confederacy." He proposes Ephthalite origin for Pashtuns. According to several scholars such as V. Minorsky, Ghilzais, the second largest Pashtun tribe, is the admixture of Afghan tribes (descendants of Epthalites) and Khalaj people.