Recommendation letter process I'm going to apply for a PhD position and as you know, I need my current supervisor recommendation letter.

So, I asked my supervisor to give me a recommendation letter regarding all the researches I have done in his lab. He responds that he won't provide any recommendation letter directly to me or any other student, but instead he will send a recommendation letter to any professor/university who asks about my progress. 

To be precise, he told me to send an email to the professor I want to send recommendation letter for and tell him to request a recommendation for me.

The whole process looks problematic to me, for many reasons:


I can't ask my new supervisor to ask my old supervisor to ask for a recommendation for me...I feel like my new supervisor won't do such a thing because there is a really tough competition between candidates and most of them already have strong recommendation letters.
I have to apply via a webform inside the university website. The apply form asks for at least 2 recommendation letters (in PDF format). There is no place in that form for me to add my professors email.
I didn't see such process anywhere, almost all my friends got their recommendation letters from their previous professors.


My question here is that did I miss something? Is this process looks okay in academic world or its just me that feel its wrong? Why my professor is not directly providing a recommendation letter to any student?

Edit
I'm living in Iran and I'm going to apply for a position in Sweden.
Having the letter of recommendation (LoR) writer send the LoR directly to the institution to which you are applying is indeed the standard procedure in the English-speaking world and increasingly beyond. In this procedure, the LoR is confidential; only the issuer and the recipient(s) should normally see it.

The process works as follows:


Online forms usually have two "sides". The first side is for you, the
applicant. You enter the name and email address of your LoR writer,
after you have obtained their approval. An email will be sent to the
LoR writer with a link to "their" side of the website, to which they
can then upload the letter and perhaps additional information.
For the offline process, you write your application, and the LoR writer sends in their LoR independently from you before the deadline. 


However, in some countries (until recently e.g. in Germany and Austria) a different procedure is used, in which the LoR is handed to the applicant who then submits it together with their application (via website or offline).

I would contact the HR department at the institution where you are applying and ask for clarification, then talk to your LoR writer again. If the institution explicitly requests that you hand in the letter, you can just relay this information to your supervisor. You may also want to make your supervisor aware of different traditions of LoR writing in different countries. Alternatively, ask the HR department whether they can accept a LoR directly from your supervisor.