Is empathy teachable? In my opinion yes. Just think about it. When you were a baby where you all concerned about other's feelings. No you weren't, as a matter of fact when I was a baby I was a complete buttnugget. I was a fat blob that just ate, slept and crapped himself. When you took a massive dookie in your pants were you concerned about your parents feelings, no you weren't. But as you grew up, you grew to accept others feelings. You grew to understand those around you and to be friendly to your peers.
When you go to school you grow friendships with those you can relate to. You start to empathize with more people as they do to you. To learn empathy is like to learn how to walk, everyone is capable of it. Empathy is taught by experience through life, not by any one person.
When you are born you have yet to learn empathy, but as you expose yourself to the real world the world itself will teach you to feel and understand others.