Exit immigration asking for destination and potentially having the ability to deny a citizen the leaving of the country

Let's say A1 is the “first-world¹,” B3 is the “third world,” you are citizen of both, it’s legal to have both, and you are not on some kind of watchlist.   I’m not a hundred percent certain, but my suspicion is …

If you are trying to go from B3 to A1, and you show the A1 passport, no one you encounter knows you also have a B3 passport, and therefore no reason to interfere with your trip to “your own” country.

If you are trying to go from A1 to B3, and you show the B3 passport, no one you encounter knows you also have an A1 passport, and therefore no reason to interfere with your trip to “your own” country.

Of course, if you are on a watchlist, who knows?  Or in one of those countries where everyone is effectively on a watchlist.

¹Where is the “second world”?

• Airlines check passports and visa because they may be fined if they bring unauthorized travelers. They will try to get the money back from the traveler, but that might fail. They are concerned with the right to enter the destination, not with the right to leave the origin.

• Airport Security check identity documents to try and catch people who may be a security risk on the flight.

• Emigration controls may check passports and other documents to keep track of people leaving the country. They are concerned with the right (or duty) to leave the origin country, but not usually with the right to enter the destination country.
  Exit stamps on passports verify that visitors did not overstay their visa, but that mostly matters for the next application. Only a few countries will detain overstayers who want to leave, but most make a permanent record of that.

According to international conventions, no country may deny their citizens the right to leave, provided there are no criminal investigations, military service obligations, etc. They can of course check that there are no open warrants, and people don't have the right to enter another country, so the right to leave theirs can become meaningless.

During the Cold War, the Communist countries tried to stop their citizens from traveling to the West. In theory travel was possible, but in practice an ordinary citizen could not get the necessary permits. And this still happens in places like North Korea.

Most "3rd world" countries check their citizens' documents before leaving for two reasons:

1) To make sure they're not on a (international or national) watch-list. Like you said, a person could be on a watch-list for various reasons such as criminal charges, terrorist watch lists etc.

2) To make sure they have sufficient documentation for their onward journey. This is to make sure the passenger has the correct visa and to check for forgeries and impersonations.

All countries with exit controls will check how you entered when exiting. This is to make sure you did not violate the terms of your visa/permit. A dual-citizen will have to present the "3rd world" country's passport when exiting--there is no way around that.

Some countries--such as Uzbekistan--require exit visas for their own citizens to be allowed to leave.

If your country allows dual citizenship, you should show both your passports to prove you have permission to fly to your destination. If it doesn't, you will might be able to get away(although in some countries this may be a criminal offence):book your flight to a destination where you are allowed to travel visa free (or have a visa) on your "third world" country's passport. Then check-in again from there on your "1st world" country's passport.

Other than that, "normal people" should have no problems leaving their countries unless their documents are not in order.