Isn't that the same thing? When you care about someone, don't you put yourself in their shoes?

I imagine most would agree that the phrase "live through their kids" has a negative connotation and "caring about someone" does not.

Fair enough, I'm probably in minority. I don't see anything wrong with living through the kids, for me it's just one way to explore the world.

Imo there is nothing wrong with it, but only if you are truly "exploring the world" in a sense of being an observer and trying to take in what your kid is experiencing, while providing advice and guidance if needed.

Where it starts being wrong is when people take "living through my kids" as "controlling and demanding my kids live the way I imagine I would have wanted to live, if I was in their shoes now".

Note: when I say "kids", I mean someone's children who are already adults and have their own life to live. I am not trying to say that kindergarten-aged children should be given full freedom to make their own life decisions and that any attempt to infringe on that is wrong.

I think a lot of the negative connotation comes from the type of parent that's trying to live out old glory years or missed opportunities through their child by forcing them into a particular sport or activity instead of allowing their child to grow as an individual.

I think that's a very smart way to explore the world, but I think with the premise of "living through your kids", you're forgetting to live yourself.

This is the actual definition of empathy, yes, not the currently trendy use which is much closer to sympathy in the way it is used.