This person first thought to any question is to react that the other person wants something from them. An example. If you ask them if they want to go to the store that person would say I'm not paying for anything. Or if if you want them to hang out they say do I look like an ATM you are always trying to get me to spend money! Or they would answer you just don't want to spend your money on gas. They don't give you a chance to finish your thoughts or intentions they just group you in a category.
I think the best way to refer to them (politely) is guarded. (Cautious, reserved, suspicious - from various dictionaries.)
The second definition of cynical describes this attitude:
2 : having or showing the attitude or temper of a cynic: as
a : contemptuously distrustful of human nature and motives <those cynical men who say that democracy cannot be honest and efficient — F. D. Roosevelt>
b : based on or reflecting a belief that human conduct is motivated primarily by self-interest <a cynical ploy to win votes>
So, you could say, "He is a cynic," or "He is cynical."
What springs to my mind are "tightwad" and "jerk".
I would use 'stand offish' or confrontational. It seems like this person is protecting their territory.