I agree with the other two responses.
Dealing with your own kids you start to understand humanity better. You understand your parents more, one of the funny things that happens, is you catch yourself responding to things the same way your parents did. Sometimes that's good, other times that's bad. This leads to self-evaluation. You have to ask how did I feel when my parents did this? What did I hate about my parents parenting style, what did I like?
If you don't have children, it's purely a theoretical question, the stakes are null. With your own children the stakes are the emotional, physical and intellectual health of your kids, it has to be taken seriously.
On the flip side you realize that we are all just kids in adult bodies. I see my children do things and I see parallels in my own behavior, or in the behavior of others. So not only do you understand your parents better, you understand yourself and humanity better.
Aside from getting a better understanding of human nature, you also have to start making decisions about your own needs vs the needs of others, in this case your children, and your co-parent. If your kid is throwing up at 2am, guess what, you can't just deal with it tomorrow. You start checking the weather to see does my kid need a coat, a rain coat, a t-shirt? As a side effect you start paying more attention externally. Questions like "how is my kid feeling right now?", or "why did they just do that?". Which means your empathy increases, and your emotional intelligence.
All of this presumes the ability to self-reflect. Which is something a large number of people lack, including parents. Basically if you ever see bad parents you will notice the common thread is lack of self-reflection and awareness. It's holding on to your past self which ultimately hurts your children, and your personal growth.