I find that most kids want to do cycling....when the rest of their class are doing the same. As has been said, peer pressure is a wonderful thing.
When they come to us as individuals with parents in tow it can be a different story. And it's sometimes the case that we spend as much time trying to alter the behaviour of the parents as we do teaching the kiddies to ride! You can understand the frustration a parent feels: has just bought an expensive bike for the child (e.g. £50 from Halfords...not much money to a 'serious cyclist ', but loads to someone who sees it as a kids' toy), can see all the other kids riding, has spent hours and hours trying to get his/her kid to ride and the kid just appears less and less interested.....so then we have to be very diplomatic and try to get the parent to encourage and make it fun rather than just standing there and bad temperedly shout "ride the %^&%^& thing" at the kid.
Example a: father and kid (about 10). Apparently they'd been trying for weeks with no success. Farther stands there openly complaining to us that kid is putting no effort in, is useless, etc. Kid throws bike on floor and screams "You're just a bully and I quit" before going off for a cry. So I take the dad for chat in the corner while my co-worker takes over with the kid....friendly, understanding discussion with dad reveals that the dad really loves the kid, really wants him to be able to cycle but is as much frustrated with himself for not being able to teach the kid as he is with the kid for not riding, and we agree that positive encouragement and fun are the way forward....and that if the kid gets distracted by a cat walking past then it's fine for him to go play with the cat and then come back to trying to ride, etc. Half an hour later, with a little help from my co-worker and encouragement from dad the kid is flying round the playground on his bike!
Example 2: father and kid (about 6). Father very encouraging and positive, goes through all the steps like we have shown him, but 20mins later the dad is still running at the side of the kid holding onto him. Another intervention....co-worker takes over holding the kid, while I explain to the dad that the kid is perfectly safe and can balance well, at which point co-worker lets go of kid, dad nearly has a heart attack and kid carries on happily cycling around the play ground while dad calms down and comes to terms with the fact that the kid is not going to come to any harm and that he can ride!
Anyway, I believe I've digressed! Here's a thing....you've got a kid who, despite your encouragement doesn't appear interested in the bike that you've shoved in front of them. What you naturally do next is ask them "Why don't you want to learn to ride?", it's a perfectly reasonable thing to ask isn't it. But sometimes what the kid hears is "what's wrong with you that you can't do this simple thing", and this makes them even less likely to want put any effort in. So why not ask something like "what can we do to make this more fun?".
It's also worth having a go with the British Cycling "Ready Set Ride" stuff, which intersperses time on the bike with fun activities off the bike that will help them ride. This isn't meant as a linear course that you follow through all the stages, rather as a set of tools from which you pick the bits that will help you and your kid.https://www.britishcycling.org.uk/go-ride/article/20180523-goride-news-Get-your-kids-on-two-wheels-with-HSBC-UK-Ready-Set-Ride-0