You are right, Ukraine doesn't need the approval of Russia, however, becoming a member of NATO is only possible if membership does not affect security of any other country. That's written on paper and one of the conditions. But since the US politics is against Russia (for some _stupid_ reasons - do a research and educate yourself), Ukraine becoming a member of NATO is a direct threat to Russia.

Edit: I also want to add to this that the US is completely aware of the situation. They know exactly that their decision not to stop the expansion leads to a war. First, the US is not stupid. Second, there is a great example - Georgia, where war for the exact same reason took place. So, who's to blame here? Is it really Putin? My common sense tells the opposite.