Can you manufacture a situation for the 5 boy, 5 girl case? Because I can't.

You could argue that it if it holds for 25 boys and 25 girls, than it holds for two equal and odd amounts of boys and girls. Of course 1 boy and 1 girl does not work though.

Here is the 3 case. Boys=1 Girls=0

0 0

111

Now try to place the last girl.