"Use up" = take so much, that something becomes empty of what is being taken. In the case of people, to exhaust them so they are made quite weak. Love is not a material, so if it's the only thing you want you should be able to continue to have love without using the person up (empty/exhaust them).
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.