First Filter
This is probably a useful story for people to know actually, it's got a ton of history to it.
There's this cosmic entity called the Phoenix. Super powerful, capable of destroying worlds sort of thing. For some reason a couple of the mutants (Jean Grey and Hope Summers) are natural hosts for it. It seeks them out, they're basically the only ones who even have a chance of controlling it... but not a great one. Jean was dead because of it for a long while, so the next time it turned up it was going to go for Hope. Understandably this made people nervous, since Jean was an incredibly talented trained telepath and Hope was a sixteen year old girl, so Steve went to talk to Scott to try to convince him to put Hope in protective custody. But Scott was already making plans because he thought that if they could control the Phoenix it would be the saviour of the mutant race, there was only a few hundred of them left at that point and no new ones had been born since the rest were killed, which is a completely different long story. So he wasn't really inclined to listen to Steve. I wasn't there so I honestly don't know how things started, but it ended with sides drawn and open hostilities. Knowing both of them, I'd bet neither of them were completely blameless. Scott will say that the Avengers wanted to kill Hope, and he might even believe it, but the only one who ever suggested that was a mutant himself, and Steve shut him down.
Anyway, it ended up on the moon for some reason and Tony tried to carry out a plan the science guys had come up with to destroy the Phoenix before it could try to take over Hope. It didn't work, the Phoenix split into five and took over five mutants. They promptly used their crazy enhanced powers to turn the world into a utopian dictatorship and then all went insane. More and more mutants started joining a resistance movement, including Hope, and finally she managed to take the Phoenix into herself and actually did do what Scott hoped before getting rid of the Phoenix. I'm glossing over a lot of details but that's the bare bones, pretty much.
So on the space cruise somehow they found out that the Phoenix was around and it was looking for Jean. The ship was having technical problems and we were sending out people in shuttles to look for help, so they decided instead of telling anyone they could get themselves all on the same shuttle and just find the Phoenix instead and deal with it themselves. Rogue actually told us what was going on while they were still out there, which I think they were pretty pissed about when they got back. Scott claimed that it was the only thing they could do because the Avengers had proved before that our solution was just to kill the host, even though none of the Avengers on board were actually the same people and even though everyone from our world knew now that Hope was fully capable of controlling it. (They did not bring Hope with them to find the Phoenix, by the way.)
Obviously it's still a big sore spot between the X-Men and the Avengers, even though no one from your world did anything wrong. But the mutants tend to be defensive because so many people hate them back home, which is actually completely fair, just... Scott's especially prickly about it and will never admit any of it was his fault even though he basically turned into a terrorist for a while afterwards and then got murdered for it. or that the Avengers weren't totally the bad guys. It's easiest to get on with him if we steer very very clear of the entire subject and avoid looking like we want any say on anything they do. Normally, Rogue is one of the more reasonable ones.