The ethical system that embraces human’s inclination for self-preservation would be the natural law. It is the body of laws that are derived from right reason and nature. It is what is considered ethically right. Hope this answers the question. Have a nice day.
That is true according to the Yerkes-Dodson Law
You can care for yourself while caring for others by simultaneously looking out for each other. For example, you can both eat vitamins to keep your bodies strong.