Could be wrong, but I always saw the relationship between Leon And Mathilda as a paternal one.
Mathilda came from a very damaged home, one in which she felt marginalized if not outright neglected as evidenced during the scene where she first encounters Leon after her family is slaughtered; the only person she feels any loss for is her baby brother.
Leon is the stoic hitman who's come to terms with his lot in life, lonely (or alone) by design, keeping to routines of Spartan simplicity until "business" has to be conducted where his only rule is "no women, no kids."
Suddenly this child in dire need is thrust upon him at a very tense moment, and even then, he considers what it means to upset his routine to help her and get involved. He reluctantly takes her in with the plan to offload her when appropriate, but circumstance dictate that that's to be later rather than sooner. They form bonds as he begins to feel "something" outside of cold, methodical calculation in pursuit of his profession again, and she begins to experience what it feels like to actually matter to someone, to be cared for.
Now, I'm not a young girl, but I've heard tell that young women from troubled homes/situations often try to compensate for damaged emotions and mental states in sometimes not so healthy ways, one of them being unmerited (and unwarranted) attraction to those who demonstrate value in their particular emotional voids, and that can lead them to further misconstrue their own feelings and act inappropriately. There's no doubt Mathilda loved Leon, but I think she misinterpreted it as the romantic love between a man and a women when in fact it was her desire for the love of a father. She tried to prove herself a worthy "lover" by demonstrating her adult side with romantic intimations, obedience, and even wanting to learn to be a "cleaner" like Leon. And I think for Leon's part, he intuited this in some way (being a stranger to certain softer emotions,) but I don't think he was reigning in any unethical desire to requite or take advantage of her; you see in the scene I posted, he's visibly uncomfortable with her sultry advances, and this moment is used specifically to add levity to the otherwise austere film. I think his struggle was more with the idea of his life being irrevocably altered, for the better, having to care for this child he's grown to love as a surrogate father.
I guess if one wanted, they could read into their more intimate exchanges and interpret under/overtones of pedophilia, but given the general universal praise for the film with some not-so-small names in it, I doubt they could have passed that one off as a [then] modern day "Lolita" without a lot of controversy.
TL;DR? Leon loved Mathilda as a daughter he never knew he could handle, and she him as the father she never knew she could have.