My girlfriend says she won?t stick around if I keep hanging out with my female friend?

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So me (23m) and my girlfriend (26f) are having an issue with my friend (25f). Jane my girlfriend, does not like the fact that i go and hangout with my friend Cassie by myself. I told Jane, that I don?t have any feelings for Cassie and that I have never had a sexual history with her as well.
Cassie and I were friends before Jane and I started dating. Currently it?s been a 5 1/2 month relationship with Jane and I?m really in love with her.
The issue got brought up, because one weekend, Jane was busy and wanted to be alone. She wasn?t answering my calls and was acting cold through text messages. So I just planned my weekend and hung out with friends. One day, being a breakfast outing with Cassie.
When Jane and I finally talked and I told her about my weekend. She was like ?how do you think that?s ok?? and I was kinda baffled. She also said ?you realize she likes you and don?t play dumb?. At the end of all of that she said ?she would not stick around for that?. Too me, that insisted she didn?t trust me and that I would date Cassie, in the end. I don?t feel anything for my friend other than a friendship.
Extra facts about Cassie: Mostly hangout with her in groups and only have hung out with her 3 times total by myself.
The weekend Jane was being cold. I told Cassie she wasn?t really talking to me. Cassie just said that I was probably overthinking it, which I thought was friendly advice.
Sometimes we text and FaceTime.
Please let me know if I?m starting something bad here? I love Jane, but I?m not sure if maybe being Cassie?s friend is a good idea or not? Maybe, hanging out one on one is a bad idea?
If you need more information, ask.
TL;DR Girlfriend wants me to stop hanging out with me female friend, because she believes Cassie likes me. Am I starting something bad?
Thanks in advance!


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