If we put general species information, you need at least ~500 genetically diverse individuals for a species to be able to safely come back from near extinction so if they're the only two Titans left then pureblood titans are effectively extinct. If they are able to interbreed with other races then for the sake of continuing Titans as a species (even not fullblooded) they'd want as many non-Titan partners as possible which the guy would be a better fit for the job... again assuming different species even can interbreed.
And if there are other options then she doesn't really have any reason she has to go with him.