Ask HN: What would you do?

Sounds sketch... but you already got paid right? If so, move on and find some more freelance work.

As for their contract? Tell them you won't sign until they reciprocate the favor.

This sounds like one of those situations where everything is telling you to bail but you don't want to miss out.

How many hours have you spent thinking about this contract?

You're talking about continuing to work with them, right?

It is possible that it is just a technicality, I guess. I would probably ask them why they want me to sign their contract over my own before I just bailed on them.

My decision would then be based on both how reasonable their answer was, as well as a close reading of the contract

From their perspective it's probably as reasonable for you to sign their contract as for them to sign yours. That said, you should definitely read and understand what you're signing, suggest revisions before signing, and pass it by a lawyer. I'll admit though, I am comfortable not consulting my lawyer for some things and it can make it easier to negotiate when you can send the contract back immediately with revisions (I've in the past struck parts of overly broad non-competes, agreements to help in any future litigation or patents, agreements to jurisdiction on disputes, gag/disparagement clauses, etc).

Just keep in mind that many actions by a startup can be attributed to "we just don't have the money". Meaning, they probably had enough money to pay a lawyer to draw-up/review the contract they're asking you to sign...while they dont necessarily have the money to hire another lawyer to review yours.

I wouldn't be offended, just read it carefully and try to work with them.