Should I give up on him?

Anonymous
Alright, so I’ll start this off with saying that I’m a 20 year old woman with no prior relationship experience. I started college a few months ago and I met this cute guy that eventually became my friend. A month after meeting him, I had a feeling that he liked me and I like him too. He asked my friend if I hated him which gave me a clue as to how I came off to him, and I needed to change that. I started flirting with him thinking he would catch the hint and this went on for about a month now and I couldn’t take it anymore so my friend decided to tell him that I like him. I only agreed to tell him because recently, he started talking to other women and I thought he was leading me on so I had to make my stance clear. He told her that he doesn’t know how to feel because he did like me at one point but then he gave up (in a month?) and he kind of already knew that I liked him. I’m taking it as rejection at this point and felt as if my flirting took me nowhere. He also told my friend that he feels uncomfortable noticing my jealousy when he plays with or hugs other women which is honestly because I felt like he was toying with me. I wouldn’t feel insecure if he just asked me out because I’d know I have nothing to lose. Question is: should I give up on him? Is he really unsure of his feelings or is he just being nice in the way he’s rejecting me? I’m conflicted. It hurts a bit but I’m not acting on my feelings simply because he stated he also doesn’t want to lead me on or force himself to like me just because I like him.
Should I give up on him?
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