For me it's usually, "I enjoy fanworks about their relationship." Everything else is optional; there are certain relationships that I love to explore and read and write about, even though I feel fairly sure that they're doomed in the long term for whatever reason - because they're unhealthy, or because I feel like the characters involved would probably move on after some point in time. This pretty much applies to friendships as well as romances, too. Sometimes it's just fun to put a few characters together and see where it goes from there, and sometimes it's gone in places that's even surprised me at the end of it all. (I'm going to have to write a Ashley/Liara ship manifesto someday just to try to explain that obsession to people, just as an example.)

Since I'm not sure it's clear: I am an inveterate multishipper. Even for canon ships which I really enjoy and have huge trouble imagining not together, I can enjoy works which have them with other people, the creator just has to try harder to convince me. And for many of my favourite ships, there is no canon romance, and as long as the canon friendship is acknowledged I can happily ship all sorts of combinations...

This accurately describes me as well! I've actually shipped quite a few pairings that really have no canon basis at all - they were explicitly a result of me putting two characters in situations that never quite happened or were shown in canon, and then realizing that I liked their dynamic and wanted to explore it more thoroughly. I do at least want to justify things in canon, or else by creating some kind of alternate universe (see also: my attempts at crazy Homestuck shipping.) But just because I enjoy one pairing doesn't mean I can't appreciate them in stories with other people, as long as the story is well-written and believably characterized.