Reb Chaim replied that the son should honor his father. The person asked that since both the son and the father are obligated to honor the kohen, the kohen should have precedence (discussed in Yevamos 6.). Reb Chaim replied that honoring a parent is a matter of pikuach nefesh because the Torah says that for this mitzvah, one will live long.
The Tur Ha'aruch writes on the words ימיך יאריכון, that the way it is written indicates that your parents will cause you to live long. This is because if you honor your parents, they will daven that you live long, so you can continue to honor them and to help them, and their tefillos will cause you to live long.
7. The Lev Simchah (Gur) zt'l said that each person comes to the world with a quota of time that he will live, and the time that one spends with kibud av v'em isn't part of the cheshbon. Whatever time he spends honoring his parents will be returned to him.
Reb Mordechai Moskowitz shlita from Ashdod tells that when he was sitting shivah for his wife, who was niftarah after four years of battling the infamous disease, the doctor called to wish him condolence. The doctor said, "Generally, I don't call to do nichum aveilim. I'm busy with my many patients. But your wife taught me a lesson in emunah, so I felt that this time I should call." The doctor said that when she first came to him, he told her she had six weeks to live. She replied, "I will live longer. I'm not worried. I have insurance."
"What type of insurance do you have?" the doctor asked.
"I take care of my elderly mother in my home, and the Torah promises for this mitzvah long life."
For the next four years, she continued caring for her mother, even as she was struggling with her own debilitating disease. There was a month that the nurse who took care of her mother was out of town, so Mrs. Moskowitz cared for her mother that month, the entire day, all by herself. There were times she didn't see her children, and she didn't see herself; she was devoted to her mother's care. This kept her alive for four years, although throughout this time, the only medication she took was a simple pill.
The Chasam Sofer zt'l (Drashos, vol.2 p.362:) writes that, at times, children think they shouldn't honor their parents because it takes away from their time to study Torah, which is the greatest mitzvah. Therefore, the Torah promises, ימיך יאריכון למען, that you will live long. If you honor your parents now, Hashem will grant you a long life, and you will have even more time to study Torah, daven, etc.
