Learn English – Replace “future work” with a phrase in three words

There are several issues.

Firstly, some simple ones: it should be publication in a journal, not on; and the process as a whole is usually called peer review, not peer reviewing. [Edit: a third "correction" removed after Colin Fine convinced me it's not needed.]

Secondly, the form …requires to go through… is incorrect. Requires is never followed by just an infinitive in English — it can be followed by either a gerund (the necessary action), or a noun phrase plus an infinitive (the person/thing who has to do the action, plus the action):

Joining the army requires passing a physical exam.

Joining the army requires you to pass a physical exam.

Thirdly, as Adam points out, there’s a slight clash in your sentence between the verbs bringing (whose subject is the author) and go through (whose subject is the paper itself). Given the form of the sentence — the verbs aren’t literally parallel — this isn’t quite a matter of grammar (to my ear) so much as of meaning. Something like

Bringing an article from draft to polished publication in a scientific journal requires it to go through a process called “peer review”.

is grammatically quite correct, parallel to eg:

Sending your daughter into the army requires her to pass a physical exam.

But it’s a slightly awkward phrasing, making a shift in agent that really isn’t necessary. So in the end I’d suggest something like:

Bringing an article from draft to polished publication in a scientific journal requires putting it through a process called “peer review”.

I think this is probably a question of style, not grammar. The grammar is perfectly fine. In my experience it's not worth trying to persuade supervisors that your grammar judgement is right and theirs is suspect, though. Probably not wise just before a thesis submission either!

It may well be that your supervisor feels that someone else will object to this style and so is anxious on your behalf. I think they probably feel that a co-ordination of a thing and a (human) personal pronoun is a little informal ( - I don't agree). However, you may want to put something like supported me in my work, which is the kind of phrase you see a lot in acknowledgements and so forth.

Good luck with the viva!