My boyfriend won't let me break up with him

Katherine
Me and my boyfriend have had issues for over a year now. I eventually just got to the point where I know I wanted to break up with him, but didn't know when or how because we have been together for three years. I was 18 when I got with him and I hadn't initiated a breakup since I was a freshman in high school. All my other breakups ended with cheating so it was easy but this was really hard. He's very needy, says he's lonely but I'm the cure to his loneliness which makes me uncomfortable. I'm in university and I study, a lot. I don't have the time that he requires to be happy and he refuses to hang out with me while I study. Which is fair. But then he gets mad about it and takes it out on me and then flips it around on me by saying that I think he's a bad person and I just can't handle that all of the time anymore.
Well then I met this guy and me and him just clicked, like it was nothing. It was so natural and the chemistry is nothing like I've ever had before. I developed a crush on him and he told me he liked me so this solidified my decision to break up with my boyfriend.
So I told my boyfriend on more than one occasion that clearly we aren't happy and I told him that I think he should try finding another woman who can dedicate the time he needs to him. His response is "no you're my soulmate". I thought that was very obvious that I thought we should have a break. I even said that I need a break because of my depression and it's not fair to either of us to be stuck, but he insists on not doing it. There's several more than two occasions I've told him we should break up and he refuses.
I told this guy about all of this and he said he understands and is happy either way. I thought maybe I'll just do what I want since I tried breaking up with him and he won't let me, which he said was fine. I ended up cuddling with him and I thought it made it clear that there's this small attachment there still that I really don't want and he seemed fine with it until not long ago that it got brought up and I think it upset him. I understand that but I thought I made this clear with him and now I feel like that messed that up but like... am I not supposed to move on with my life? I even told my boyfriend that I cuddled with him and his response was "cool", like he didn't care at all! I thought that was going to be the end of it for him and was part of the reason why I did it, and just cuddled because I didn't want to start a big cheating thing. I'm so stuck now and just don't know what to do.