So many reasons that ring true for some and not for all:
- It's zany. Especially fixed. Just makes ya laugh.
- It's mentally simpler. On my commute congestion is bad enough that if can shift, I'm constantly shopping for the right gear.
- It's mentally simpler. On a longer ride you can just get in the zone.
- It's mentally more responsive. When I'm not shifting, I just think the way I want to ride. If I need to squeeze in a little place, it's almost like I'm sort of tip-toeing through.
- It's less maintenance.
- It's more durable. Especially fixed. It's the only bike that won't freeze over in the winter. Even when the grease in a freewheel is chilled to a viscous lump and brakes have turned to blocks of ice, you can still get around very effectively fixed.
Those are the big ones, I think.