Nostalgia.
Doing things the old way. The additional challenge of hunting with a traditional type muzzleloader. Anyone can be even a halfway successful hunter with a modern firearm. However, it simply takes better hunter skills, better marksmanship, more discipline, and more patience to be successful with a muzzleloader. This is especially true for squirrel hunting. There’s simply something unique about using a patched round ball to shoot game. The unique smell of the cloud of smoke from black powder, the unique report of the rifle. Basically, doing things in the same basic fashion as they did over 200 yard ago. Best way I can describe it is, you just have to experience it to fully understand it.
Also, I like the old things. Steam locomotives, old cars from the 30’s, radial engine biplanes, antique furniture, coal oil lanterns, old knives, and especially old muzzle loader rifles. Yes, even the replicas.