Can’t men just identify as women to avoid the draft?

No, changing your gender identity doesn't affect your selective service registration

I'm not sure why you're getting downvotes for this because it's a pretty straight forward question with a non-obvious answer.

Ever tried to actually "change your gender"? It's not really a thing you can do any more than "becoming gay" if you are straight.

Thots these days belong to the streets not the family unit. Send them to the meat grinder. We can stand to lose a few 19 year-old egirls who contribute nothing but thirst and workplace drama. Burn through a quarter million breeding age and females then we can talk about societal norms and replacement rates. Actually, how about whenever an FTM commits to being male they sign up for Selective Service.

I believe in the specific case of gender equality, the burden of proof is on the side which claims that discrimination is justified.

The genders are not equal, you're operating on fictional premise.

Well that's a bit daft, as men and women are as different as green and blue.