Dude, it's the original relationship of the show, taking up the better part of over three seasons. They broke up Finn and Flame Princess in the show just so he could one day get back with PB, and then never had him and PB get back together. She's his Mary-Jane, his Lois Lane, his Princess Zelda, whatever way you wish to put it, she's the one girl that he had been trying to date the longest, with the most history, having spent the first 57 episodes of show winning her, only to have their relationship cut short in "Too Young". It was even originally intended for PB to stay the same age as Finn for a number of episodes in season 3 to further pursue their romance, with artist Jesse Moynihan saying he "heard" rumors that she was supposed to be young for several episodes, but things ended up changing in the production:https://web.archive.org/web/20120429194633/http://jessemoynihan.com/?p=1290
The only other girl with any lengthy history with Finn was Marceline, and they stopped making her a viable girl in like her fifth episode for whatever reason, when it was clear she was supposed to be part of a love triangle with Fiinn.
In a 2017 interview even the voice actor who played Finn suggested that he wanted Finn to finally end up with Princess Bubblegum, stating that he he wanted Finn to end up with a "Princess" at the end of the series:>"I think for Finn, it’s hard because I know things that are going to happen, but definitely just closure. For me, I’d like to see Finn possibly finally settle down and end up with a Princess, as he’s been having trouble with that over the whole nine seasons."https://metro.co.uk/2017/01/08/adventure-times-jeremy-shada-reveals-his-hopes-for-finn-in-the-final-ever-episode-6368644/