Rabbi, if a father tells his child that he doesn’t need to honor him, why wouldn’t that remove the obligation of kibbud av? If the mitzvah is about honoring the parent, shouldn’t the parent be able to waive it? What are the halachic sources and reasoning behind this?
Yes. Your reasoning is exactly what the Gemara says. ״האב שמחל על כבודו, כבודו מחול״ — if a father waives the honor due to him, his waiver is effective (Kiddushin 32a). The Rambam and Shulchan Aruch go further. They tell a father not to be so demanding about his honor that he puts his children in a position where they might fail to honor him. Instead, he should be willing to waive it (Hilchot Mamrim 6:8, Yoreh De’ah 240:19).
The distinction is that waiving the obligation is not the same as erasing the mitzvah. The Torah commands the child to honor the parent, but it also gives the parent the right to forgo the honor owed to him. So if a father says, “You don’t have to stand when I come in,” the child can remain seated. The Radbaz was asked whether honoring the father after such a waiver is no different from honoring anyone else. He answers ״אבל אכתי מצוה איכא״ — it still counts as kibbud av if the child chooses to honor him (Teshuvot HaRadbaz 1:524).
There is also a difference between not doing an act of honor and actively insulting a parent. The Rivash (siman 220), citing the Raavad, explains that the permission to waive honor does not extend to giving a child permission to verbally abuse him. In other words, “You don’t have to stand for me” means exactly that. It doesn’t mean “You can speak to me with contempt.”