This is sound advice. You have a significant amount of control over people's lives as a manager, and that should be treated with a level of respect. You have no idea how people feel, and it is quite possible that someone you manage doesn't know where they stand with you. At times that is more than enough to cause them stress and even convince them to look elsewhere. Work is stressful enough, and you don't need to add…
I do think this is something you can learn. Having a good mentor/coach helps. I had a hard time with this personally, but after all these years I've seen almost every seat be replaced (more than once, too) and I've gotten used to it. You have to become more consciously aware that a business relationship is a separate thing from a friendly/family relationship.