Well, Neo is The One because he truly believes that he is (and, as revealed in Reloaded, also because he carries the code of The One). And while it is consistent with the original trilogy that love gives power to Neo (he resurrects as The One after Trinity tells him she loves him; he becomes the most OP when Trinity is in danger, etc.), there is nothing that indicates that Trinity also has some powers, carries some code or at least believes that she is also The One. She just starts flying randomly.
Also when Trinity dies in Revolutions Neo doesn't lose his power, he remains to be an almighty superman.
But then again, the movie is just a "fanfic" (even though it's written by one of the original authors) created to provide a happy ending to the franchise. I guess it doesn't have to be perfectly logical.