How do I stop feeling like I have something to prove?

Usually in friendships or relationships I always act like I’m obligated to act a certain way to not make the other person feel like I’m too gullible. Im afraid of intimacy but crave the feeling of being understood. But I give nothing to the other person to help me because I don’t want to appear pathetic or vulnerable. Yet whenever anybody tries leaving me I pathetically beg for them to stay even tho i know i won’t let them help me and that the relationship (although never stated by the other person) is draining for them.