Why do clubs have to be very close to each other to have a big rivalry ? Brighton is considered pretty close to South London anyway
They don't, it can come through regularly being in competition with each other as well, like Arsenal and Man U 10-15 years ago, or Leeds/Cardiff/Millwall for obvious reasons. It's just that Palace and Brighton don't seem to have any factor that promoted an intense rivalry.
According to the internet, Brighton is only 36 miles from Croydon. So it's not that far-fetched, a lot of clubs have rivals at a similar distance.
RAC Route Planner (Shortest Route): AMEX Stadium to Selhurst - 43.92 miles AMEX Stadium to Fratton Park -50.17 KC to Elland Road - 56.00 I didn't say it was a strong reason/