You must get 4 badges before you can challenge the Petalburg City Gym.
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You beat the TRAINERS first then the doors unlock and you can go through them ^^
You can challenge the petalburg gym after you beat fire type gym leader in lavaridge town.
Beat the gym leaders of:RustbroDewfordMauvilleLavaridgeThen return to petalburg and Norman will accept your challenge
The fifth gym is in petalburg city
Petalburg City.