Why can't I select any cards for my brawl?

Did you check what fray you are fighting in? The most common situation is that a player has been assigned an Alpha/Beta fray or a Gold Foil fray when they do not have any eligible summoners to use.

There may also be a rare scenario if you are battling in a Chaos Legion only fray. Right now there is only a single Chaos Legion summoner available for each splinter. So if you are in a Chaos Edition only match in an enemy arena where only 1 or 2 splinters are available and your opponent has banished the only allowable Chaos Edition summoners, then you will not have any summoners available to choose from.