How do kids learn empathy?

I see a lot of parents of young children trying to teach empathy or teach kids to be empathetic by the parent telling their child how their child's behavior impacts them (the parent):

"When you said that, it hurt"
"That hurt my feelings"
"I'm sad that you did that"
"Don't speak to me that way, that's hurtful"
"What you said was mean and unacceptable"

I see how we could get to thinking that this would work. But it won't.

That's not teaching empathy. That's teaching them that the parent's feelings matter more than theirs. The parent is pulling the "that's mean" card instead of empathizing with the underlying reasons why the child was "acting out" with "mean" or "disrespectful" behaviors.

Empathy can be defined in many ways, but the way that I like to define it is like this: I'm able to hold onto myself enough to be present with you and your experience which allows me to feel into the situation and guess what you're feeling just enough to be able to ask the right questions so that you feel safe to tell me what's really going on for you.

In that case, wouldn't it be more helpful for the parent to say something like "You must be really angry to be saying something like that, I'm here for you, what's going on inside honey?"

Now that's empathy in my book.

Kids don't learn empathy by being asked to prematurely give it to others, but to EXPERIENCE and FEEL empathy.

This is what sets the foundation for them to be able to hold onto themselves enough to be present with others when they're developmentally able to. And then to truly be with another.

Modeling and giving empathy is what works.

What would you add? What has your experience been in learning how to be more empathetic? Please share below in the comments!