I'm the same, I don't want kids of my own and I'm glad, now, that I didn't have the round-the-clock burden, as I don't think I could have handled the stress. But I'm "good with kids" and have had responsible care-time with a ton of nieces, nephews, and worked as a nanny for older children. Kids of all ages seem to like me and I like them as long as there's a "handing-back-to-mom" point in time.
I did go through a phase many years ago, when both my parents had just died, I happened to be married at the time, and I longed for us to start a family; I got a very, very primal, strong urge that seemed to be triggered by this surge of generational emotion from losing the family of my own origin, and getting this massive, basic sense of a need to create my own new one. I think that was a profoundly "instinctive" thing that kicked in, in my brain and hormones, and rising out of deep loss and grief.
It eventually passed and I'm okay again now with not having any.
I also think that because I was made an Auntie from a very young age, due to being the youngest of a large family who all grew up and had babies that I was looking after even when I myself was still a kid too, I'd "seen enough" lol!
I seriously was at such close range of not just observation of my siblings being parents in all its challenges, but also was responsible for those kids too, taking them places alone, etc, that I almost felt like I'd had a small window into a glimpse of it and didn't need to do it too. Other people's kids in my life kind of let me know I didn't want to go that route myself.