> It means "you can assume the family does not have two boys".

But it does not mean that you can assume that p(you're told at least one is a girl | both are girls) = p(you're told at least one is a girl | they aren't both girls) as explained by 6gvONxR4sf7o.

If you allow assuming whatever you want, then many answer are allowed!

That’s what it means that the problem is not “well-posed” as mentioned by in_cahoots. You need additional assumptions to get a definite answer - and the answer will depend on the assumptions.

As JeffJor noted it seems much more natural to have assumptions that keep the symmetry of the problem (because why not?) and the answer 1/2 is not just possible but arguably “better”.