I did not know I would enjoy fatherhood, but I suspected I would and I wanted that in my life. Turns out, I was right. It is hard to explain, but here's some points on my side:
I love telling my kids stories at night. They are getting too old for it now, sadly, but for years I would lay with them in bed and make up stories about forests and magic rocks and other fairy tale stuff. The stories were all terrible, but it didn't matter. We would laugh so hard some times, even now we joke about things we made up in those stories.
I taught my kids to make movies. They make a few per month, and every year we do a huge Christmas video with a script, voiceovers, advanced camera work, original musical score, etc. watching them learn and take on more and more of it each year is incredibly satisfying. You feel proud when you see it.
We intentionally mess up the words to songs to make them funny. One time my 5 yr old son sang "I'm very glad that he's my FATHER" (obviously DAD would have been the right word there) and we all lost it. I also have a specific song for each child, where I can substitute their name for the name in the real song.
We are hungers, so we give each other hugs at night and call each other stink face before hitting the sack.
Teaching my kids to play sports/music is super fun. It takes time and tons of patience. But seeing them progress in these intricate skill sets is immensely satisfying.
In the end, I'd say my enjoyment is directly correlated to my time and emotional investment in fatherhood. I took night duty with all of them, every night, so my wife could sleep. I changed their diapers. I watched them on weekends so my wife could go on girls getaways or whatever. And of course she watched them and took care of business when I was in grad school or working. Joint effort. But that time invested is what makes the parent relationship work the best.
But that is all just me, and everyone is unique. Some people will not be into their kids and can find these kinds of avenues for satisfaction in other pursuits. And they should probably not have kids, and that should be perfectly acceptable.