I think he's saying that challenges shouldn't be based on houses because if you can't get a teammate, you can't participate. This is obviously true whether or not it's based on houses, but if, for example, there are 5 badgers and 7 serpents, there would be two people kicked for not having a teammate, but if they were allowed to team up, nobody would have to be kicked. It's not fair for people to not be able to attend a class purely because they don't have friends, or they struggle to make friends. It reminds me of the Some Room for Improvement post a while ago by a banned player, in which they mentioned an 'elite' group of players. I think this is similar to that. People who aren't in a group of friends would struggle to find a teammate, which then means you can't go to the class.
I have a feeling that this will be declined, because challenges are 'supposed to be about houses going up against each other, and you get housepoints as rewards' but I don't think that that's necessary. I don't see why a winner can be from a different house to another. If you are with a teammate from another house, you wouldn't throw because then your house doesn't get points. Yes, it would probably be preferable to have teammates from the same house, but kicking people for not having a teammate when there are other people also being kicked for not having a teammate just because you're not in the same house in a bit extreme.