Over the Garden Wall has turned into my Halloween show. When I last watched it, I realized something. That's not surprising. OTGW is packed full of hidden details. I watched a couple of those "What you missed in OTGW" videos and while I learned a lot, I've never seen this topic covered.
Spoilers
In the episode at the spooky tavern, they introduce everyone by their profession. Butcher, Baker, Midwife, etc. They ask Wirt what he is, but Wirt says that he doesn't like labels. I think Wirt just doesn't know how to identify himself. That's why he thinks everyone at school doesn't like him. He has no self-confidence because he doesn't know who he is. When the people at the inn come up with a "label" for Wirt, he's very proud of it. It finally gives him that sense of identity he was missing.
Also, it bugged me that the tavern-keeper's song had so much important information. I hate it when songs have essential information that isn't mentioned anywhere else. It's hard to understand and absorb an entire song the first time you hear it. In this case, the song says that the Beast wants to turn people into a tree to use for lantern fuel. I totally missed that, which diminished the impact of the finale (I had this same problem with Frozen 2 - "not too far or you'll be drowned." That was incredibly important, but it was buried in a song so I never got it during the first viewing).
But there is something else buried in this song which was important for Wirt. The tavern keeper says "don't believe his lies." When Wirt faces the Beast in the last episode, he's about to let the Beast put his brother's soul in the lantern. But Wirt very abruptly stops and changes his mind. He realized that the Beast was lying. If he didn't discover that (presumably from the tavern-keepers hint) he would have been trapped there forever. And Greg would have turned into a tree.