Great question Carlo and I'm sure one that will invite a whole host of answers.
I cannot remember a time when I wasn't on a bike, as it just seemed to make sense as a kid that this was the only way you could feel liberated, and get a speed thrill until you were old enough to get a car.
Of course, for the UK in the 80s there came the BMX explosion which linked bikes to fashion and street cred, but as this waned most of my peers drifted away from bikes as girls and engines came into view (don't worry - I was distracted by girls aswell). However, I still had the passion and viewed it as more than a means of getting from A to B. I got my first ATB in the late 80s and haven't stopped changing bikes and regulalry cycling on and off road ever since.
In addition to the obvious health benifits (one of the best aerobic workouts, less strain on joints and heart than running/jogging etc) it lets urban dwellers escape to the countryside, whilst also leading rural types (like me) to see their surrounding landscape from a different angle, getting a real feel for terrain and topography from the rise and fall of the road, and seeing nature and the changing seasons over the hedgerows, experiences denied to car drivers screaming past in a lower position.
I don't personally race (although will ride out with pals recreationally now and then), so don't get a directly competitive buzz from the sport, but feel that it is a great way of challenging oneself, for example to cycle further and faster each time which can lead to an enormous sense of accomplishment. It is also a sport that does away with the hassle of travelling to a pitch, hanging around for a dozen other players to get ready, enduring pathetic and forced agression and the communal dissapointement of a losing side.
It is also a sport for all, from the muscle-bound to the stick insect (in fact you will observe from the pro tour circuit how the stick insects dominate), with age or ability no barrier to one's enjoyment, or how you are respected and treated by others in the cycling community