This question reminds me most of Abraham Maslow's hierarchy of needs. According to him, we all must attain self-actualization, which translates to the phrase, "What a man can be, he must be". Although there is nothing wrong in doing your best to achieve your full potential, this attitude sometimes results in selfishness, as there may be times when you will think that your own needs and interests are far more important than others'.
I also do believe that humans are inherently selfish. In fact, psychology says that in the absence of coercion and restraint, human beings will act and behave the way they want to. This premise, in itself, is selfishness. In as much as we want to consider other people in making our decisions in life, truth is, we are more inclined into satisfying our own well-being. This behavior is also manifested in other organisms; however, it is in human beings that this trait is culminated.
Therefore, it is both nature and nurture that drive humans to be selfish.