I certainly can't speak for other artists. Maybe it's true for some artists, that their paintings become part of the family, their children, birthed from their creative womb. So perhaps they form some deep emotional bond with it that way. But I can only speak for myself.
Do I have a hard time letting go of my paintings?
The short answer: No.
Why not? Why do other artists get so attached to their work and I don't? The reason I don't get attached probably has to do with the reason I create art. You often hear people talk about art as a form of self-expression, emotional expression, or whatever the current term is. But, to be perfectly honest, I do not create art for the purpose of expression of any kind.
What! You're an artist! Isn't that the purpose of art, to express oneself?!
Honestly, I don't even know what the heck that means! Express myself? What does that really mean??
I'll tell you why I create art. Not for self-expression. I create art because I want to share beautiful images with other people. If I'm not sharing my images with people, or they don't think they're beautiful, there's no point. I have no desire to paint images just for myself. If I could sit on a deserted island and just "express myself" at the easel all day, knowing no one would ever see any of my work for all eternity, I'd rather just go fishing.
To me there is no purpose to art if it can't be shared. My reward for creating art is not self-expression. My reward is the satisfaction of knowing other people are deriving pleasure from it. I want people to see it, become emotionally stirred by it, and get some sort of enjoyment or pleasure from it. If I paint a picture of a horse, and someone tells me they have to buy it because it reminds them of their wonderful childhood summers riding horses on the uncle's ranch, that is far more gratifying to me than simply creating a painting of a horse because of my own love of horses, or love of painting.
That said, there are exceptions. I do occasionally become somewhat attached to a painting under certain circumstances. This is usually a result of having achieved some milestone in my skill development. For example, I did get a little attached to this fox pup painting when I finished it.