This is not weird at all. I would not want to share my therapist with anyone I know (hell, ideally, I wouldn't want to share her AT ALL).
There is no reason to feel selfish imo: this is an important part of your life that you want just for you and it's perfectly understandable and as you pointed out, it could get weird if you happen to mention stuff in your session to your acquaintance and she compares it to her own sessions, or the other way around, etc.
To me, the idea of my T having other patients is disagreeable so I like to keep these people as abstract as possible.