I think Arsenal wouldn't be a perfect place for Rodrigo because Arsenal already has good wingers, and if they sign another winger the it would be hard for them to used Rodrigo in X11 sheet. Manchester city left wing is already empty after the departure of Jack Grealish and so in Manchester City he has a higher probability of playing in the X11 sheet.
Arsenal has Madueke and Martinelli who played at the left winger position at this moment. I'd call Rodrygo is dumb enough if he goes there. The better he goes to the City as this club has only Doku who played at the left wing, and obviously lack of depth. So the new player like him will be needed there.
I hope he is not going to the wrong club. City is best place for him.