Altruism (coined by Comte) is defined as "the selfless concern for the welfare of others." A little more clearly, it means doing x for y and not expecting anything in return. But is that possible? Can one genuinely do for others without expectation of reciprocation?
The classic example is giving money to a homeless person. What are is the true motive? Do you do it because you feel sorry for the person and want to help them out? Or do you feel guilty? Or do you do it to make yourself feel better? Can you ever really know the real answer?
Hume's belief that people are altruistic because of love is void. And he did it himself. Hume believed that people love others and feel sympathy for them and are thus altruistic. If you are sympathetic to someone, your actions are not altruistic. What you do benefits both of you. It helps the person and it relieves your angst about their condition.
Kant, being Kant, further warps altruism. He believed that there are universal laws (hi religion) and because of them we are required to help anyone we can. He took the onus of self-serving want off the table and placed it upon the universe. But in doing so, he complicated matters. To summarize the position, we help others because there are universal rules that say we must help all those we can help. But in doing so we relieve our angst at not following universal law.
Davidson and Haack have applied complex mathematics to try to solve the problem of intent. And really that is what altruism boils down to. The basic argument is that a person helps a homeless person not to help that person and not to give themselves satisfaction but for a more complex reason, possibly that the person is ashamed that his family is rich and intolerant of the homeless. And still, we are relieving ourselves of angst.
In the end, altruism does not exist. No matter the angle we approach it from, we are relieving ourselves of angst whether we do it consciously or not. We demand something in return for our act of "selflessness". We do it because we need to because in the end we are narcissists at our very core.