I don't think anyone is trying to force their child to ride.
In my case, I had a kid that WANTED to ride but was scared to do so. As her mother, I know what she wants... every picture she brings home from school has her on a horse, every books she checks out at the library... are about horses, first thing she shows all her new friends is all her horse stuff (particularly her new saddle that she is now terrified to ride in).
Monday, I told her that if her homework was done, I'd take her with me yesterday when I was riding. She talked about nothing else for two days, except going with Mommy, feeding Mommy's horse, brushing Mommy's horse, can Mommy's horse wear the purple polo wraps? Can she ride Mommy's horse? Arrived and she brushed my horse, she shoveled corrals with me, watched me ride, set up obstacle courses for me, fed the resident pasture ornament more treats than a horse should probably eat and then when I got off and told her to hop up and walk my horse out, she freaked. Wasn't that she didn't want to, she was scared because my horse was "big" and had an English saddle on (she's ok in a Western right now, terrified of English saddles because that's what she fell in).
I got her up there, took some effort but once she was up there and had a person on each side of her walking along, she was fine. I KNOW my kid and I know that the minute something seems difficult she gives up. She needed to get up there and face her fears instead of giving up immediately. If she gets up there a few more times and decides she doesn't want to any more, that's fine. I'm not going to force her to do something she hates but I'm not going to let her give up on everything just because it got difficult.