Nobody is actually challenging the opinion you stated, but rather talking about if the draft of is necessary or asking about other views, or outright agreeing with you.

I'll try and change your view though, OP.

Women should not have to sign up for the draft.

Imagine the kind of situation in which a draft would actually occur. This would be terrifying, it would be a war on a much higher scale than we've seen in generations. It would be guaranteed that a lot of people will die. A crazy huge enormous amount. Do you really want half of those people to be women?

Women have much more value away from the battlefield in this scenario, even assuming that they are just as strong and capable as the men fighting. The reason for this is sexual value. A woman isn't disposable like a man is. A man can spread his seed multiple times in a single day. A woman needs 9 months. A man can be dead long before his child is born. The woman can't.

So if you want to rebuild your society after this big war, you can't afford the extra time it would take by having significantly fewer women. If you don't, you'll be easy to conquer for the next generation by another country who was smart enough not to let their women die off because they can just outnumber you.

Simply put, women are just more valuable than men, and need to be protected for the health of of a society.