My motivation is, as others have said, simply because I like it.
But since I started again a couple of years ago here in and around Liverpool, I've found a new side to it in discovering so much more about where I live. (The bulk of my cycling in my youth was in other places).
Liverpool is a fairly small city, with pretty good (and relatively inexpensive) public transport, and that's the way I've been getting around here for years. I don't have a car, but I do travel as a passenger in other people's cars too. Those are great ways of getting to a destination.
And for years I've been like that, less than inspired to take up cycling again because it just didn't seem anywhere near as nice here as when I used to cycle round Hampshire and Dorset - New Forest, Purbeck, Jurassic coast and all that.
But since I've been back on my bike, I've been discovering so many beautiful bits of countryside, pretty villages, architectural beauties, lakes, country lanes... and I never even knew most of them existed, despite having been born here almost exactly 60 years ago.
The development of off-road cycle routes has been an eye-opener too, and the Liverpool Loop line is my most used highway now. And the Leeds-Liverpool canal does a sort of semicircle around where I live at a distance of only around 4-5 miles - and I'd never seen it before, other than crossing it by car at places north of the city (and occasionally stopping for a short walk along it). I now use it as a route into the city when I feel like taking the long way round - and by including the waterfront, I can reach the two ends of the Loop Line for a really nice circuit of the city with very little on roads.
Further afield, when I lived here in my teens, one of my cycling destinations was Southport - there were some quieter diversions, but the A565 isn't the nicest road I've ridden. Now I can get there and back on two different NCN routes which are mostly off-road, with a number of variations in each direction.
And across the river, I can ride the waterfront route round the end of the peninsular, then follow the Wirral Way, across the marshes, and then the Dee path into Chester - again with almost no roads.
If those things weren't originally my motivations, they are now!