The most probable reason is that your Pokemon are hacked. For example, if you had 5 legitimate Pokemon and 1 hacked, you will not be allowed to participate.
Check these basic things for hacked Pokemon:
Moveset: If they have weird moves, such as Roar of Time on Magikarp.
Place of origin: Like finding Mew on Route 1.
Stats: If a Magikarp had a 500 attack stat.
Level obtained: If Eevee was caught at LV100.
Poke Ball it was caught with: Like a Bulbasaur in an Ultra Ball.
Egg Obtained (If it hatched): Like if you got an egg from your rival
Egg Location Hatched: Most common would be hatched at ------.
Egg Level Hatched: Magikarp hatching at Level 100.
ID: There are certain IDs that are famous for hacked Pokemon.
OT: There are certain OTs that are famous for hacked Pokemon.
Ribbons: Hackers like to put every ribbon on a Pokemon, which is not possible.
Shininess: Some Pokemon cannot be shiny, such as Zekrom.