I think the problem is that when you view the flipped image, you see it with "new eyes". Take a master painting and flip it, and it will look funny to you (if the masterwork is a familiar one).
Holding a piece of art up to a mirror has the same effect, which is a trick known to masters over the centuries. It's not just you. Everyone has the same "problem" to some extent. One of the great masters (Can't remember which) said to "hold your painting up to a mirror to see its ugliness" (His words. Not mine)
The proof of this comes when you post the two versions of the image the way you did. Most people can't tell which is the original orientation. You perception is prejudiced by having looked at the original so intently for a long time.
Another way to see the work with new eyes is to set it aside for a few days, then look at it again. I wish I had done that with the self portraits I posted. They were quick drawings that looked fine to me before I set them aside for a while. Unfortunately, I had already posted them.
