Help with closeted bi

So I met a guy (let's call him Jack) back in October initially just for regular hookups. We ended up liking each other to a greater extent to the point where I ended up spending thanksgiving with him rather than the friends I usually go with. He's in his 40s, works, and is bi although he has not come out. From the beginning he did tell me he was not seeking a relationship because he could never walk in public with me holding hands nor do normal relationship stuff. I didn't have a problem because at that time I was also not seeking that. Even so, we started texting each other often, and spent almost every weekend together at his place. We usually hang out and then have sex and I stay at his place.

Towards the end of the year, there was a big incident that occurred with someone else and he was there to comfort me. But after I went home for winter break, I decided that when I'd go back to school I would focus on classes and try and not be off campus so much. So I told Jack that I needed space while I got over my situation and needed to focus on school. So I didn't see him as much. Then one afternoon I texted him asking if he wanted to meet up and he casually mentioned that he was going out on a date with his gf so he couldn't.

Long story short, he was seeing her for a while and I was not sure what to do because she did not know about me and I felt like it was cheating but he said it was not since I was a guy and not another woman. So I agreed to keep seeing him but just to hang out and no sex, and he reluctantly agreed. One of those days we hung out he casually made a comment about how he preferred to be around me than her and hoped we could get together more often when she was out of town/busy. I realized then how I was second and I didn't say anything but it stuck with me. He had told me not to worry that she wasn't going to be around much longer since he didn't like her much while he did like me. He said she wasn't the one he wanted to be with but a friend pointed out, "So what he meant is once he finds the right one he will just dump you?". He also took her out to places to eat, the movies, and other places. With me he was rather cheap. I'm not saying I was looking for a sugar daddy but the one time we did go out, he took me to the mall so I could buy some things I needed, we almost went to a restaurant but it was a bit crowded and so he said it'd be better to go home and cook and it'd be more economic. He felt the same about going to see a movie or other things which he felt were a waste of money but at the same time seemed to do with her.

Eventually I met with him one day to break off with him completely because I didn't like how he was treating me second even though I had met him before his gf and every time he spoke about her it was in a negative tone. But that day I was going to break it off he told me he had just broken up with his gf the night before. When I told him how I was done with our situation he said he had been expecting this and he completely understood if I wanted to break it off but at the same time she was out of the picture so if I stuck around, he'd have more time so we could spend the summer hanging out and doing some of the activities we had been planning. He did admit having dated a guy a long time ago, in secrecy. He agreed we could be something more than friends with benefits but not a relationship since he could not be openly with a guy. He also said he would be considerate next time if he did meet another woman and let me know in a manner other than casually.
I've a lot more to say but I've written enough. I basically don't know what to do. One thing, when we first met he lied about his age and I found out later. He thought it wasn't a big deal but I still think about it. Then the other weekend, we were talking about something and he accidentally said "My current gf" but then gave me a look and then said "I mean the one I just broke up with" and continued. It had crossed my mind, a friend had also said, that perhaps he had lied about having broken up with her and maybe he is still seeing her as well. I don't think that's the case though because he has been around a lot more, although maybe I was wrong. This past Sunday he dropped me off because he told me he had to go to his office to get some work done (some refunds he has to process or something). The point is, not long ago I met a jerk that for the first time I could not get out of my head and was more open sexually with him than anyone before. It made me realize how much stronger my passion for a guy can be and made me wonder what it is I feel towards Jack if a complete stranger I hooked up with had me feelings these powerful feelings for him. I don't know if I should end things with him.