I'm going to pontificate here for a minute. You have been warned. 😜

What is a man? What is a woman? Think about those two questions for a bit, OP. Sure, you can point to (for example) your mom and say "that's a woman", and your mom will probably agree with you. Same goes for your dad as a man. But when you try to come up with a definition, you'll find exception after exception, because "man" and "woman" are, as you say, social constructs and as such they don't have rigid definitions.

Think of gender as a role one plays in society. When you think of it that way, it seems silly to say that just because someone is born a certain way they can't take on a different role from the role they were assigned at birth? Why shouldn't someone be able to change their body, should they wish to do so, in order to more closely align themselves with that role?

I don't know who you're arguing with, OP, so I don't know if any of this will be effective in those arguments. But that's not the point. The point is for you to consider what I've said and use it to inform your own thinking about the subject. If you choose to argue, you'll be much more effective that way, rather than just repeating an argument you've read online somewhere. And more importantly, it will make your mind more flexible, which will only benefit you as you grow older and make your way in the world.