My girlfriend says I'm too soft and that she dislikes that part of me. Can this relationship work?

ChrisTorez
The argument we had was because of an incident that happened earlier in the day. We were playing a sports game with 2 other friends for fun and once it was my turn to be paired with my girlfriend, she refused. She asked to play with another guy whom she has expressed interest in romantically. She said she plays better with him and doesn't want to play with me at all. This has happened multiple times in the course of us dating. I never paid any mind to it before but we were just playing for fun today with friends and I thought it wouldn't matter if I played with her. By the way, we are all evenly matched. When she did this, I felt rejected in front of friends and didn't want to show it so I just kept those feelings in.

We've had arguments like this in the past because of her inviting guy friends over during the night to hang out with her. She doesn't seem to understand how this would make a boyfriend feel. I've talked to her about it and I just decided to let her do what she wants since if she wanted to cheat, she's going to cheat regardless of what I do. She was clearly bothered by me expressing my feelings each time I did.

Later in the evening I talked to her about it but she did not have any comments at all about it. It wasn't until I asked her to speak up did she say anything at all. She told me that she hates this soft/sensitive side of me. I'm glad that she was finally honest to me but this was quite a blow to how I felt about this relationship. I asked her why she dislikes that side of me and she tried to backpedal knowing what I was going to say next. She wants me to stop being so sensitive and soft and I agreed, but I know that's impossible. It's how I am and she doesn't accept it. I brushed the idea of us separating and she nearly cried.

After what happened, I don't think I can think of her the same way again. I also feel like she doesn't actually love me anymore after what just happened. I want to make it work but does she want to make it work too?
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Well, she called me earlier today to ask why I didn't text or call her (I was busy with classes and study groups). She thought I was still mad but I just forgot about what happened.

Well, it seemed like we're all good but she doesn't seem to want to cuddle in bed like we used to. Not to mention she warned me about me not cheating on her or else she'll go with her "second choice." A person who she said sent a "cute" message and picture she is using as a phone lock screen.
My girlfriend says I'm too soft and that she dislikes that part of me. Can this relationship work?
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