That friend may be one of those who is empathy challenged. They aren't emotionless - their own emotions and problems are ultra important - but they see other people as an extension of themselves and other people's problems as an annoyance to be put up with until they can talk again about something important - themselves. You will meet these people your whole life. They can be acceptable co-workers, if you watch your back, or team members, if you have someone to rotate in when they split, but they will never be adequate friends or lovers. It isn't a reflection on you, except your patience, that you have this type for a friend. Just know what they are capable of, and take care of yourself. You wouldn't go hiking with a legless friend (unless they had their prothsesis or a wheelchair - see, double amputation is much less of a handicap that heartlessness) and don't seek support from a heartless friend.
I draw the line between children and adults: for a heartless child, I will move the earth to help them reconnect empathetically with the human race. For adults, I have to let them be. And do not try to share my innards with one who will be indifferent to my guts.