(I offer this information to give folk an idea of how the XMen first formed in the comics. The
XMen team formed in comics in 1975.)
Xavier first meets Wolverine when the nutter that is Logan is(Sorry, I’m British and we say ‘nutter’) is in his yellow spandex. As Wolverine meets his Canadian government handler for a meeting, Xavier enters office and joins the meeting. Xavier offers Logan a place on the Professor’s XMen, and the freedom to be his own person, rather than being controlled by government. When his Canadian handler threatens Wolverine if he leaves Canadian control, the issue is set for Logan and he walks out alongside Xavier.