First of all, it isn't a blanket statement... meaning, he isn't saying this will be the case for all of His people all the time.
Second... the words "own household" is key. This is not a young man living at home and his parents are on him all the time. Because it says, "his OWN household" then this is speaking about a man who has left his parent and now has others under his authority... wife, children, servants, etc.
Third... even if this was tied to his parents... (which in this case of this verse I don't believe is the point).... the idea of "honor" means "to place great WEIGHT on."How could you "honor" a parent who stands against you, your faith... your family? By not demeaning them by taking that position... by turning the other cheek and walking away without hurting them.
Remember these verses:
Matt. 5:23 Therefore if you bring your gift to the altar,
and there remember that your brother has something against you,
Matt. 5:24 leave your gift there before the altar, and go your way.
First be reconciled to your brother, and then come and offer your gift.
Most read this wrong... it isn't that you had something against him and are going to make it right... the brother has something AGAINST YOU and God expects YOU to go make it right with HIM.
What a plate of humble pie that is, right?
Anyway.... I don't think the verse you shared is including parents because they are not under their child's authority... it would have been written "their household" not "his household." But even if it was... you can tell them you love them and walk away and that does not dishonor them.