Am I the jerk for cutting off my friend?

For context me and my friend have known each other for 3 years and we're in high-school. Recently someone started a rumour about me and everyone starting giving all my friends dirty looks just for being near me. My friend said she couldn't handle it and didn't want to be friends anymore. Which was fine. I respect her choice. The problem here is she still wants to "be close but not be friends" and I'm just like no? Either you're my friend or you're not. I told her unless she still wants to hang out like we used to then I'm not going to talk to you like I used to. As simple as that. She went really quiet after I said this and I want to know if I'm being to harsh.