When saying "I love you most" to someone after they've said "I love you more" shows that the one sending "I love you most" love the other person more than considered possible
When your ex says that they love you like a friend, but they constantly tell you that they love you just to get you to say that you love them too in hopes that you really are still secretly in love with them. Even though you broke up six months ago. Most common in ex girlfriends, but can happen with clingy-stringy ex boyfriends as well.
Carrie : I love you.
Frank : I love you more.
Carrie : nope. I love you more, look it up, it's on the internet.
Frank : how about that, you're right, it is on the Internet.