But I guess, the easy story is, when Hope came into play, we were about a decade out on a cataclysmic event which decimated Earth's mutant population from thousands to about 200 and dropping. Hope was the first mutant born in the years since that event.
And because of that, attracted the attention of a lot of groups with different designs on her. Purifiers looking to destroy her, opposing superheroic forces looking to contain her potential. You and that idiot you hang arou Deadpool took her first and you took Hope into the timestream to raise. I guess for about sixteen years on her end, about nine months on ours.
So for all intents, she sees you or at least a Cable, as her father.