He raises some good points, but then, the judge raises some interesting objections as well. The fact is that providing a false date of birth would be a piece of misinformation with a considerable number of negative effects. This is so regardless of whether providing false information regarding one's sex might also cause a considerable number of negative effects.
Is it really a "false date of birth" if he identifies as someone born on April 27, 1969?
If the birth certificate says that he was born on that date, yes, is is a false date of birth. Why?
I'm not sure what you're getting at. If you're saying it's some other form of falsity, I would agree it implies (together with known facts) a lot of other false things that are relevant in assessing his life history, and those of a number of others. Hence, my point about a lot of other complications.
Now, if he merely claims to have been born on that date but it is not in the birth certificate, sure, that's still false.