This one is kind of a bad look for Everett, but I also kind of sympathise.
I read this as the woman doesn't want to play the game and the other men are insisting that she ought to join them. In her point of view, she'd spoil the game, and I guess Everett also agrees with her.
Whist is a game that requires teamwork and strategy. The new player will likely be overwhelmed by the rules involved - there's several gotchas in the cards you're allowed to play each turn - and be unable to appreciate the grander strategy or really participate in the co-operative aspect of the game.
If the woman genuinely doesn't want to learn the game and these men are insisting she ought to play, then the men could be setting up a situation where they can feel superior for knowing the rules. I've definitely been invited to learn to play a game with friends just to get absolutely dunked on, and it isn't a great feeling.
If the woman does want to play and these men are eager to teach her, then Everett is really being a jerk here. If you view teaching new players a game as a waste of time then you'll eventually run out of people to play with. It's also not fair to assume she doesn't have the sense to remember the trump, but I suppose with new players that's often a real gotcha in the game.
One thing that I appreciate about these comics is that the common theme is that either Everett is a champion of the oppressed, or he speaks his mind about things he feels strongly about. So I guess I prefer to think he's sticking up for the woman although I admit it's at least equally likely that he just doesn't want to play with a newb.