From His Holiness the Dalai Lama:
...we all have a feeling of closeness to ourselves. Even in cases of apparent self-hatred, some kind of self-cherishing attitude lies deep within us.
It is from cherishing oneself that one can gradually extend a similar attitude to others. Even animals have...altruism, particularly those whose offspring depend on them for a period. Naturally, there would be a bond of special love. So this love, this natural feeling of appreciation, comes from a biological need because the structure, the formation of the body, is such that you are compelled to depend on love. In order to survive, we need to care for one another. We already have the seed of love or compassion or affection for others because we have affection for ourselves. That is the seed.
The question arises, how to develop infinite altruism? It seems that it is possible to develop infinite altruism through wisdom and intelligence. Normally, when one talks about the need to cultivate love and compassion for others, one feels that this will be of benefit and help to others, but of no help to oneself, or irrelevant to oneself. This is a mistaken viewpoint because when you develop love and compassion for others, you are able to mentally develop profound satisfaction and courage. As a result you, the practitioner, benefit. You will have less fear, more willpower, more self-confidence. Automatically, one mentally becomes calmer.
--from Many Ways to Nirvana: Reflections and Advice on Right Living by His Holiness the Dalai Lama, edited by Renuka Singh