> Now we have paradoxes like > Russells paradox > Banach-Tarskin paradox
Though Russell's paradox and the Banach-Tarski paradox (note the spelling in each case) are reasonably called paradoxes, they are paradoxes in two very different senses.
In the Russell case, a contradiction arises from a few very reasonable (or at least reasonable-seeming) assumptions. Therefore one or more of those assumptions must be rejected.
In the Banach-Tarski case, assuming the axiom of choice leads not to a contradiction, but to something unexpected. If you find that unexpected thing actually repugnant, then reject the axiom of choice. Otherwise accept that the unexpected happens. Some mathematicians do reject the axiom of choice, but I do not know if any have done so because of Banach-Tarski.
I suspect that a good many, on first hearing of the Banach-Tarski paradox, thought 'Wow! How about that! Isn't mathematics fun?' And perhaps: 'So what happens if Choice is false? Do any loopy things happen in that case?' Meanwhile, note that if set theory is consistent, one may safely assume either Choice or its negation.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting