Imagine an AU, where Odin does not get to pick which of his sons get to be King. Pretend, whichever one of them wed’s first, gets first dibs. (Since they will already have a Queen, and be on their way to making an heir.)
Odin arranges for a Princess from (insert realm) to come to Asgard; her sole purpose is to meet Prince Thor; in hopes of being wed. Odin is still trying to give Thor the throne, unknown to both Loki and Thor, in the process. The girl likes Thor; she thinks he’s nice and they hit it off beautifully, until Loki comes home. The moment she sees Loki, she cannot help but be smitten with him, completely forgetting about Thor. Loki starts out trying to get her attention as a game. He thinks it would be funny to make the woman Thor was supposed to marry, fall for him instead. Loki plan backfires and he ends up falling in love with the girl, realizing she was actually very smart and nothing like the typical princess that he had met before. Odin finds out and he is less than pleased, even though technically, it shouldn’t matter. Odin tries everything in his power to separate them, including threatening to harm Loki if she doesn’t leave him and marry Thor instead. Frigga finds out about Odin’s threat and helps them escape to elope, knowing that once they are married, Odin can do nothing to change it and Loki will be King; as he rightfully should.