I actually agree with YourLocalJesus on his first point.
It would make sense to also feel hate towards someone you love. You would hate to lose them or hate to have them as an enemy. You hate how vulnerable and exposed they make you feel but want that at the same time. And of course what you share is special so you become jealous when a threat to what you have enters into the equation.
When I deeply care for someone there is a whole melting pot of emotions underneath it all. But, people like this are few and far between.