English speakers sometimes start a sentence with "Sure" in an argument. They use "Sure" sarcastically. Instead of being a way of agreeing with the other person, it shows that they can't believe what the person has just said.
A: Nina, I need to use your car. Let me borrow it, just for a few hours.
B: Sure, I'm supposed to let you borrow my car, when you won't even pay for my dinner? No way.
In this example, Person B does not want to let Person A borrow the car.