I don't understand this "playing a different person" as being some kind of automatic preference. The ratings are just about equal and youre doing the exact same thing with a rematch as you would be with a new opponent. And seeing as the amount of variations in chess are astronomical, it doesn't seem reasonable than any two games between any two players (especially on lower levels) will be the same. So subtracting the "newness" of the person (you're playing against positions, not just people), what is so preferable? Once again, I have so say a bit of fear is creeping into your desire to "run" from one opponent to another, who, if you didnt know their user names, you wouldn't be able to tell was a different person to begin with.
The difference is that my only agenda is to play someone. I could play this person who asks for a rematch or a could play someone new. Someone new is the tabula rasa .. I have now idea why the already played person wants to play again... revenge? show off? who cares. I don't care if my opponent is a master or a beginner. I'm pretty used to losing so the idea of "fear" is something in your own mind. There seems to be a bit of transference going on, but who knows?
Read my other responses. There is no practical difference between the player you just played and a "new player." The only difference is in your mind where you prefer not to play players who are out for "revenge" or some other motive. Would accepting a rematch for whatever reason, assuming they haven't been abusive, REALLY be that harmful for you? The fact that you consciously choose to not play again does say something about your psyche, I believe, and the idea that "you just wanna play new people" doesn't seem to answer it.
I love how this guy keeps arguing against himself. Yes, there is no point to a rematch. I am glad you figured it out, now move on.
I often don't have time to play 2 games.