The relationship between parents and children forms one of the deepest foundations of human existence. Harming this bond is a severe moral failure, carrying a public curse meant to echo throughout the entire nation. At its core, this offense involves treating one's parents with disrespect, disgrace, and shame [רש״י, אבן עזרא, ביאור יש״ר].
The primary approach among commentators is that this specific list of curses focuses on sins committed in secret. Disrespect toward parents typically happens behind closed doors in the home, far from the eyes of witnesses. Because it occurs in private, an earthly court cannot catch or punish the offender [אור החיים, רשב״ם]. Furthermore, parents themselves usually hide the abuse. They choose not to make their child's disgraceful behavior public, either out of deep personal embarrassment or because they are entirely dependent on that child [מלבי״ם, ביאור שטיינזלץ]. This hidden harm can take many forms, such as a child dodging the duty to care for their parents by using false excuses and trickery, or showing disrespect through a slight comment or even a subtle hint [ביאור שטיינזלץ, ברכת אשר על התורה].
The placement of this warning directly after the prohibition against idolatry reveals a deeper truth about human existence. There are three partners in the creation of a person: God, the father, and the mother. Consequently, a person who rebels against and disrespects their parents is viewed as rebelling against the Creator Himself, who formed and raised them [קיצור בעל הטורים, רלב״ג]. This leads to a natural conclusion: if a person who disrespects flesh-and-blood parents brings a curse upon themselves, the same is certainly true for someone who angers and disrespects their Father in Heaven [שפתי כהן].
Beyond the physical family, the concepts of father and mother carry a broader meaning. Any person who commits a shameful act damages the honor of the nation's founding fathers and mothers—Abraham, Isaac, Jacob, Sarah, Rebecca, Rachel, and Leah. On a wider allegorical level, the father represents God, and the mother represents the congregation of Israel. Therefore, any shameful behavior done in secret is ultimately a dishonor to God's name and a direct insult to the people of Israel [מלבי״ם].