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. This will show that you cannot select any cards for your brawl. 

This may also happen if you battle in a Chaos Legion Only fray and are in an enemy arena that has banned a summoner. There is only one 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 - you will not have any summoners available to choose from.