Should my girlfriend be upset that i have a female friend from before i met her?

So i have this friend from highschool who is female, i am male. I ve never had any interest in her i never even thought that might affect my relationship but when i pick up the phone if she calls or simply mention her in casual conversation my girlfriend fights with me about it. It s really frustrating because i could see how it could be upsetting but at the same time it seems unfair to tell your partner they can t be friends with someone if there s nothing wrong with it.In fact i never even hangout with this friend i only chat with her via text every so often and i let my girlfriend have full access to my phone, meaning she could even read our messages if she s worried and my girlfriend has looked into my phone multiple times looking for something but never found it yet this problem persists. I m at my wits end. Should i break up with my girlfriend who i love or cut out a friend to keep her?