So I don't think the actual problem Luke has with monogamy is related to "assuming ownership of another's sexuality". It might be more along the lines of "assuming responsibility for another's sexuality" or "presuming participatory status in another's non-solo sexuality", but I'm not sure.

I interpret it as "here are some verbal symbols I can use to manipulate my feelings about a given subject via a vaguely associated other concept that I have a certain emotional affect associated with". It certainly isn't something that follows logically and nor is it useful for myself. But evidently it is a useful diff to apply to Luke's previous mental state.