I think if you look at your situation, you will agree that you do share in others' emotional experiences (as empathy involves concern for others and their well being). Take your grandfather, for example, as you have a lot of worries for his current health situation.
With animals, there really isn't a lot to think about as you just naturally tend 'to accept them as they are' and bond with them. They love without condition and that is very attractive. They don't talk back and do make it quite easy to love them.
I think some people in your life have let you down but it is best not to categorize all people as uncaring. I do believe that most people are good. I also believe that one needs to separate himself from those who are not good.
Your life will improve as you add good people to it and reject the bad people as being unworthy of your time and attention.
