Someone demanding your passwords to prove you care is asking for control, not proof.

A demand for your passwords is not a request for reassurance, whatever it is dressed as. Trust cannot be produced by handing over access, since what access gives is the ability to check, and checking has no end point because there is always another thing to look at. Framing it as proof of love puts you in the position of having to disprove something. That framing is the part to pay attention to.

You are allowed to say no without offering some other proof. If it keeps coming back, tell an adult you trust or a friend outside the situation. Someone who respects you will not need the login.