To hold the lives of others as more important than one’s own life is to be altruistic (otherism).
Quoting philosopher Ayn Rand, in her essay “Faith and Force: The Destroyers of the Modern World,” published in Philosophy: Who Needs It:
“The basic principle of altruism is that man has no right to exist for his own sake, that service to others is the only justification of his existence, and that self-sacrifice is his highest moral duty, virtue and value.
“Do not confuse altruism with kindness, good will or respect for the rights of others. These are not primaries, but consequences, which, in fact, altruism makes impossible. The irreducible primary of altruism, the basic absolute, is self-sacrifice—which means; self-immolation, self-abnegation, self-denial, self-destruction—which means: the self as a standard of evil, the selfless as a standard of the good.
“Do not hide behind such superficialities as whether you should or should not give a dime to a beggar. That is not the issue. The issue is whether you do or do not have the right to exist without giving him that dime. The issue is whether you must keep buying your life, dime by dime, from any beggar who might choose to approach you. The issue is whether the need of others is the first mortgage on your life and the moral purpose of your existence. The issue is whether man is to be regarded as a sacrificial animal. Any man of self-esteem will answer: ‘No.’ Altruism says: ‘Yes.’ “