I see this a lot but I'm not really sure I agree with the logic...
I don't see why they need to 'replace a mother.' There are plenty of children that grow up without mothers or fathers(or really any parents at all in situations like orphanages) and don't have any real negative mental consequences. The kid 'getting shit' really isn't a great argument either - it's not any different than the type of taunting kids get for being poor or fat or dumb or ugly or whatever; children will always think of petty reasons to mock one another. It's just something most kids try to do to be accepted prior to being adults, I guess.
The other thing that you didn't mentioned that gets brought up a lot is that gay parents would raise gay children, but that makes sense, since straight parents only raise straight children.
Of course in my case I loathe children so I don't care too much about this aspect of the debate, ha ha ha.