Not all moms "like" every kid event either but they do them.
Dad's "fun" should be in spending time with his child. A child isn't "his" when the activity is something dad likes and "mom's" when the activity is something dad doesn't like.
The point is not for dad to enjoy the activity itself (or for mom to enjoy it, for that matter). The point is to enjoy the child's enjoyment. Try telling him that.
If only mom takes the kids to every Easter egg roll, birthday party, ballet recital or rehearsal, play date, tae kwon do class, library story time, etc., the kids get the message loud and clear: This is mom's job. Dad only does X with me (whatever dad is willing to do).
The rest of the message: If you, the kid, are really into your dance or story time or whatever, and it means a lot to you, Dad just isn't interested, sorry, kid. Your interests that make you an individual just don't matter much to dad. When you like something that he also likes, you'll be more interesting to him. What does that model for a child? Self-centeredness.
We all want the ones we love to think we're interesting people. Even young kids know if their interests are ignored and not supported by their parents. And as much as he can say "It's great you like to do X" or "It's nice your friend Y is having a party," that means nothing unless he supports it with his presence at least occasionally.
I remember the post about dads who hated school functions and I responded basically the same way on that one. Dads who insist on bowing out of all the kid's activities, school or social or extracurricular or church, because dad doesn't "like" it are disrespecting their children as people who have some interests that aren't the same as dad's. Will dad keep this up when the kid is in middle school and is in the play? Will dad be there for that? Will dad bow out of the high school concert or, heck, graduation?
Is every kid event a delight? No, often they're chores. So dad can slap on a grin, try not to squash the kid's good time with grumpiness and grumbling, and take the kid. And give mom a break. Even better, mom and dad can both go. At the very least they can joke about it together later.
If your husband just wont' do any kid events, tell him, "Our child gets messages just from our presence or absence each day. If I, the mom, am always the only one present at all these activities, the message is twofold: I am always there to be the kid's chauffeur and dad doesn't really want to know what you do with your time. I cannot always be there to drive, so you must get used to doing that at times. And you need to do it not grudgingly or while making comments about how boring it is, because kids DO pick up on all that, and will know that you think your time with our child is not valuable and our child's activities are meaningless." Then tell him you'll work out a schedule or a deal or whatever where he takes the child solo, without you, to certain things; you handle others; and some you do together.