It puts me in the flow, in the zone.
I think it's this. I can get the same from rock climbing or hill walking or even just walking in the countryside, but cycling is what I can do easily from the door.
I'm fully immersed in the cycling with energy, focus, and enjoyment. I'm completely absorbed in what I'm doing, and lose any sense of time. Ride long enough and you enter a difference state of consciousness. A sense of well being and contentment flows through me. I'm in the now and what came before and what comes after are pushed to the far sides of my consciousness.
Now I used to think I could only get this feeling during my mountaineering. But my observations are that I get exactly the same feeling of contentment in the now from my cycling.
Yes, there are undoubted fitness benefits, but those are secondary to why I cycle. Fitness can be achieved by other means, but you are not in the flow whilst doing them.
Like
@Drago I started cycling as a child , around 3 years old, and never stopped.