I suggest that Wolverine is as much Mr. X-Men as Scott these days. That’s why they’re getting together, as a throuple or as Jean is cheating, whichever. Motivation is the same — Wolverine has what Ariana Grande looks for in a boyfriend.
BUT, there is an alternative. Maybe Jean’s getting down with Wolverine for revenge on Scott, for Emma. “Hell hath no fury like a woman scorned,” as they say. Jean could be trying to hit Scott where it hurts.
I don’t think that’s the motive, but it could be.
It could also be that Jean likes sex, a lot. The Black Queen didn’t come from nowhere. It was all about Jean’s desires, remember?
So, there’s three possible motives. I’m sure there’s more.