Drew here is actually a real person!

Taylor talks about a guy named Drew Hardwick who was her seatmate. They bonded together but Drew had a girlfriend whom he would always talk about to Taylor because he was unaware of Taylor's feelings (just like in the song!). So Taylor would pretend to smile and complement his girlfriend all the while secretly wishing that he would notice her (Oh Drew). So she wrote a song for him and years later he knew about it and asked Taylor if he still had a chance at her (no way dude! it does NOT work that way). Taylor rejected him this time (way to go!).