Do I really have to cry every time I leave an animal shelter?
What about leaving an animal shelter makes you cry?
The sorrow in their face when I say goodbye hits me hard
I'd advise you not visit any animal shelters, then. Feeling compassionate towards animals is bound to make you upset.
Nah, I would rather not be tender hearted or caring.
Maybe you would, but those are aspects of your personality and they're just fine.