Contradicting the words, statements, and opinions, of one’s parents:
One may not contradict the words of one’s parents [father or mother, on any subject]. [This applies whether one outright argues on his parents by saying something like “Not true” or “Nonsense,” or sides with an individual who is arguing on his parents, such as by saying “I agree with your opinion,” either way it is considered that he is contradicting his parents. This applies whether the father states his opinion on a certain matter, or relates a story, nonetheless, a child may not contradict his father even if the child knows it to not be true or knows that his father is exaggerating its details. Nonetheless, it is permitted for a child to make a statement which can be implied to be contrary to his father’s statement, so long as he does not explicitly contradict his father, and does not make the statement in an assured way, and says it in a respectful manner.]
Not in their presence: Some Poskim rule that the above prohibition to contradict the opinion of one’s parent applies even not in the presence of his parent. The majority of Poskim, however, rule that it is permitted to contradict their words when not in their presence. However, some opinions limit this to only Torah related matters.
Torah related matters: Some Poskim rule that the above prohibition applies to even Torah related matters, when one is in front of the parent. Furthermore, even when one is not in front of his father, such as when writing a Halachic responsa or Halachic rulings, he should not mention his father by name if he plans to argue on his opinion, and is rather to mention the name of another rabbi who holds similar to his father. Other Poskim, however, rule that this prohibition only applies to mundane matters and not to Torah related matters, of which it is permitted for a son to argue on his father. According to all, it is permitted to have an open Halachic discussion and debate with one’s father on a certain topic in order to come to a final conclusion. Likewise, it is permitted for a son who is qualified to give a halachic ruling on an actual case in order to prevent a mistake from being made, even if it contradicts his father’s opinion who is present .
Parent asks one’s opinion: If one’s parent asks them as to their opinion on a certain topic, they may express it even if it is opposite of the parent’s opinion.
May a child voice his opinion in a non-argumentative and noncontradictory manner, if it opposes the opinion of his father?
Some Poskim rule that it is permitted for a child to make a statement which can be implied to be contrary to his father’s statement, so long as he does not explicitly contradict his father and does not make the statement in an assured way, and says it in a respectful manner.
May a child correct his parents for his parents’ own benefit?
It is permitted for a child to correct his parent in a situation where lack of doing so can cause pain or monetary damage to the parent. Nonetheless, the correction must be made in an honorable manner.
May one contradict his parents in writing, such as in an article ?
So long as the contradicting statement will not reach the eyes of his father, it is permitted to do so according to those who permit contradicting one’s father when not in their presence.
May one contradict his parents after their death?
 Michaber 240:2; Rambam Mamrim 6:3; Kiddushin 31b; See Hagahos Rebbe Akiva Eiger 240:2; Beir Sheva Perek Chelek; See Pesakim Uteshuvos 240:7-9; 14; See Encyclopedia Talmudit Erech Morah Av Vaeim Vol. 42 pp. 585-589
 Shach 240:2; Beir Heiytiv 240:3
 Sefer Hamussar 5
 See Q&A!
 Shach 240:2; Derisha 240:3; Perisha 242:20; Beir Heiytiv 240:3; Shulchan Gavoa 242:41; Yalkut Meiam Loez Parshas Yisro
 Taz 240:3 that so is implied from Michaber ibid regarding Machria Devarav Befanav; Biur Hagr”a 240:3; Chayeh Adam 67:8; See Rambam Shechita 11:10 who argues on his father; Tur who argues many times on Rosh; Shut Rav Akiva Eiger 1:68; Aruch Hashulchan 240:12; Yifei Laleiv 3:9; Tiferes Yisrael Kiddushin 1:54; Chazon Ish Y.D. 149; Yad Sofer 22; Minchas Elazar 4:6
 Misgeres Hashulchan 143:2; Tiferes Yisrael ibid
 See Encyclopedia Talmudit Erech Morah Av Vaeim Vol. 42 pp. 587-589
 Implication of Taz 240:3; Rashal in Yam Shel Shlomo Kiddushin 1:67; Chayeh Adam 67:8; Ben Ish Chaiy Shoftim 2:3; Shevet Halevi 2:111-2See Rashi Kiddushin 31b; Tur 240 in name of Ramah; Aruch Hashulchan 240:12
 Taz 240:3 based on Tur C.M. 107 who argues on the opinion of his father regarding a certain matter although rather than mentioning his father’s opinion by name mentions a different opinion who held similar to his father. By doing so, he was able to honor and respect his father by not directly arguing on him.
 Beir Sheva Sanhedrin 110, brought in Hagahos Rav Akiva Eiger 240; Tzeida Laderech Parshas Kedoshim; Emek Hasheila Sheilasa 56:5 in opinion of Sheilasos; See Aruch Hashulchan 240:12
 Atzmos Yosef Kiddushin 30; Pischeiy Teshuvah 240:1; Aruch Hashulchan 240:12; Ben Ish Chaiy Shoftim 2:3; See Kiddushin 30b “a father and son who study Torah in the beginning become enemies of each other, although later become friends.”; Meiri Kiddushin ibid; See Chut Shani 240:4
 Rama 242:3 regarding a student with his teacher, and the same applies for a son with his father; Perisha 240:3; Taz 243; Gr”a 243; Sheilas Yaavetz 1:5; Cheker Halacha 243; Minchas Elazar 4:6; Nofes Tzufim Y.D. 137; Pachad Yitzchak Mareches Kibbud Ava Vaeim 42:2; Torah Temima Vayikra 19:3
Other opinions: Some Poskim rule that a son may not give a Halachic ruling which contradicts that of his fathers, in the presence of his father, even if it applies to a current case at hand. [Shach 243:3 in name of Maharik Shoresh 140]
 Aruch Hashulchan 240:13
 See Rash Mishantz Toras Kohanim Kedoshim 1; Rabbeinu Hillel Toras Kohanim ibid; Moshav Zikeinim Shemos 20:12; Beir Sheva Sanhedrin 110a; Chazon Ish Y.D. 149:1; Shevet Halevi 2:111-2; Chut Shani 240:4; See Encyclopedia Talmudit p. 586-587 footnotes 252-259
 Vayivarech David 3:10
 Sdei Chemed Mareches Vav end of Kelal 31
 All Poskim who rule that one may contradict their parents when not in their presence; See Riy Kiddushin 31a; Shut Maharsham 1:52; 2:224; Minchas Elazar 4:6