Q:

Why "objectionable" and not "objectable"?

"Objectionable" is strange because unlike most "-able" words it begins with a noun instead of a verb.
I would think it should be "objectable", ie, capable of being objected to.
What is the reason for it being "objectionable"?

A:

You are right that the suffix -able is added to verbs to form adjectives, and objection, originally, comes from a past participle: 
Objectionable (adj.):

1781, from objection+ -able. Related: Objectionably.

objection (n.)

late 14c., from Old French objeccion "reply, retort" (12c.) and directly from Late Latin obiectionem (nominative obiectio), "a throwing or putting before," noun of action from past participle stem of Latin obicere "to oppose" (see object (n.)).

-able:

word-forming element expressing ability, capacity, fitness, from French, from Latin -ibilis, -abilis, forming adjectives from verbs, properly -bilis (the vowels being generally from the stem of the word being suffixed. 

(Etymonline)
As you can see from Ngram, objectable usage has always been uncommon. 

