Some very troublesome phrase os using them.

Different adjectives just take different prepositions and constructions. Sometimes there are logical or historical reasons, sometimes not. In any case, it would take too long for you to try to find out why - it's much simpler and quicker just to learn what is right!

"Capable" can only take "of", as in "capable of doing something".
"Able" takes the infinitive, as in "able to do something".

You cannot say "able of doing" or "capable to do" - these may sound sensible to you but they are wrong, and they sound wrong to every English-speaker

Historical reason? I think it has better to follow logical and real reason the most.

All languages are shaped by their history. Words start off with one meaning and gradually they evolve, often till the original meaning is completely abandoned. But the particular constructions and phrases that they had because of the original meaning often stay with them. It is impracticable for someone learning the language to try to find out the reason in every case (especially since many of the native speakers no longer know it); you just have to accept and learn these constructions.

By the way, what makes you think that a historical reason is not a "real" reason? I would say that "it is this way because of its origin and development" is a very real reason!

Well, think about it: "capable to" does make sense. To, as a preposition, means an abstract placement before any verb. To kick, to make, and so forth. So "capable to" must be reasonable. And what preposition should I place behind adjectives, this troubles me a lot.

Language has nothing to do with 'sense' or with logic. As Syntinen has already suggested, every language develops in its own way, regardless of whether it makes sense to anyone else or not. For example, word order, too, is different in different languages. But, as an English speaker, I have no right to tell a French or Spanish speaker that it would make more sense to put the adjective before the noun, not the other way around as they do.

Like Merry Andrew says, sense and logic haven't much to do with language. Say "capable to" instead of "capable of" if you wish, but you will never be mistaken as a native English speaker.

As you move along, you will find a number of phrases in English at least, whose meanings seem to have little relationship with the words they contain. Those phrases have come to have their own meanings, as if they were one word.

collocations
Have a look at the excellent research being done on collocations by, among others, Cobuild, Oxford University Press and Longman dictionaries. They are each compiling a corpus of language from radio, television, the press and literature and then analysing and extrapolating data for word frequencies, collocations, usage etc.
When looking at words which 'go together' like "capable of", the frequency of 'capable' and 'of' appearing next to each other is so high that any other combination is virtually non-existent - and wrong.