No, that's not right. Cantor's argument says that it's impossible to create a bijection between the rationals and the irrationals. It does this by considering

No, that's not right. Cantor's argument says that it's impossible to create a bijection between the rationals and the irrationals. It does this by considering an arbitrary bijection and then showing there is at least one irrational not in that bijections image (a contradiction). In that sense there are "more" irrationals than rationals. There is another field of mathematics called measure theory in which the notion of "almost all" is made precise and in that case, yes, almost all reals are irrational. But that has nothing to do with Cantor's proof, which is pure set theory.