Dual Citizens: What does it really mean to 'exit' the US on a US passport?

But what does it mean to ‘depart the US on a US passport’?

I think they mean "don’t depart the US on another country’s passport".

Because then you have a passport mess – the foreign passport shows an exit stamp but no entry stamp prior to that, since you entered the US on a US passport… right? *

So I think you are reading some regulatory forcefulness into it, but maybe it’s just a friendly reminder not to make a "flub" i.e. mistake or oopsie. The consequence being that other immigration agents would be confused or suspicious of the spurious exit stamp (since US exit stamps are rare).

It would be an easy error – especially if traveling by air. The US doesn’t have exit controls, so I wouldn’t expect to need my US passport. Any airline will need to see my destination visa etc. to even board you**. So I’d have my destination passport ready to present, with USA passport buried in my bags. When someone in a uniform asks for my passport, a distracted or complacent (or just tired) traveler might just automatically hand it over, and not even realize they were CBP and not airline! So yeah, I could see making that mistake very easily.

You could also infer a meaning of "don’t depart the US on no passport at all", which is indeed illegal as discussed in other answers.

* Since US law requires that.

** Since airlines are punished severely when they fly a passenger to a country without checking that they have the papers in order to enter that country. Those penalties must be pretty high, since the airline makes out like a bandit – they forcibly sell you an immediate return ticket at full list price, void your planned return ticket and sell that seat to someone else.

I’m going to take a slightly different tack from Mark Johnson, whose answer is, nonetheless, essentially correct.

But what does it mean to ‘depart the US on a US passport’?

It means that you must use your US passport when you check in for a flight departing the US. However, this phrase, which appears on several official sites, mischaracterizes the law, which as Mark Johnson notes does not require US citizens to use a US passport but only to bear it. In other words, the government is claiming that the law means something other than what it says. This is not unusual in immigration law.

Some examples follow.

From https://www.usa.gov/dual-citizenship

if you have dual citizenship, you … must use a U.S. passport to enter and leave the U.S.

From https://travel.state.gov/content/travel/en/legal/travel-legal-considerations/Advice-about-Possible-Loss-of-US-Nationality-Dual-Nationality/Dual-Nationality.html

U.S. nationals, including dual nationals, must use a U.S. passport to enter and leave the United States. Dual nationals may also be required by the foreign country to use its passport to enter and leave that country. Use of the foreign passport to travel to or from a country other than the United States is not inconsistent with U.S. law.

The executive branch often adopts incorrect interpretations of the law. When this affects you, you have two options: you can go to court to obtain a ruling from the judicial branch establishing that the executive’s interpretation is flawed, or you can accept the executive’s interpretation.

Practically speaking, the executive’s interpretation in this case, that you must "use" your passport to depart the US, can only mean that you must present it to the airline when you leave the US, because the government does not otherwise inspect the passport. But there is no consequence for using a foreign passport (I’ve been doing this for years), so you are not harmed by this misinterpretation of the law and you therefore have no standing to sue the government.

And in fact, the sentence "use of the foreign passport to travel to or from a country other than the United States is not inconsistent with U.S. law" may be intended to cover dual citizens leaving the US, though it is far from clear.

If the US started insisting on dual citizens using a US passport to check in for their departing flights, and imposed conditions that created some sort of disadvantage (such as preventing them from using their foreign passport at the place of arrival), then someone will sue. The chance of this happening is fairly small, I think, but it could happen as the EU implements ETIAS and the US tightens up its entry/exit system. More likely than legal trouble, however, is difficulty checking in with an airline whose systems do not support sending different passport details to the country of departure and the country of arrival.

Another aspect of this is that there is no penalty for violating 8 USC 1185(b) (see What is the penalty for US citizens entering/leaving the US on a foreign passport?). So you’re not going to find yourself in court. The worst that could happen if you try to leave the US without a passport is that the government somehow finds out and prevents you from boarding because your departure would be unlawful (they sometimes screen departing passengers; I’ve never seen it but someone on flyertalk says it happens frequently on certain flights to places associated with money laundering). If you have your US passport, though, you can just show it, and they should let you go, even if you checked in for the flight with your foreign passport.

But what does it mean to ‘depart the US on a US passport’?

It means you must have a valid passport with you when leaving.

Just because they don’t check every single person every single time they leave doesn’t change the legal requirement.

Except as otherwise provided by the President and subject to such limitations and exceptions as the President may authorize and prescribe, it shall be unlawful for any citizen of the United States to depart from or enter, or attempt to depart from or enter, the United States unless he bears a valid United States passport.

unless he bears:

Bear definition and meaning | Collins English Dictionary:
If you bear something somewhere, you carry it there or take it there.

So, fine people of the internet, what think you? Is this wording just some legal nonsense, or does it have practical significance?

If you have a valid passport when leaving, then you will most likely have a valid passport when returning (where in most cases it will be checked).