On the one hand, N espouses that people shall almost ignore the needs of other people to achieve one's own greatness. But on the other hand he describes kindness as
"Kindness and love, the most curative herbs and agents in human intercourse".
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I assume, when you refer to his espousal of the idea that one must ignore the needs of other people to achieve one's own greatness, that you're referring to Nietzsche's ideas of slave and master morality, in particular the latter "virtue". I believe this to be an instance of the conflicting nature of philosophy and reality which yields reality paramount, solely for the sake of one's psyche.
It might be argued that Nietzsche suffered existentially his entire philosophical career; yet, such suffering was visible especially physically during the few years preceding his demise. As is summarized by many texts on the causes of and conditions around Nietzsche's passing, he suffered a "long sickness" - a period of utter desperation, pain, and melancholy. Nietzsche had, in some ways, reasoned himself into his depressive state, a result of his hyper-rational philosophy, including that which you claim is his espousal of self-centered gain. It was during such periods of sickness that Nietzsche "yearned for the emotional solace" that values such as kindness - and others that he believe constituted slave morality - offered. In short, the way of reconciling these ideas is to understand that one - motivation by sole egocentric gain - led to the other - existential suffering and the realization of the importance of communal values.