While unaccompanied bags are always a concern, you are all reading this wrong.
The OP has purchased a flight from the U.S. to Brussels and has paid the fare for that flight. It just happens to change planes in Amsterdam. But what if the flight from the U.S. to AMS is more expensive. Then, a "smart" passeger would just book a flight to Brussels but get off in AMS.
The airlines are wise to this. They have contracted with you to fly you to Brussels. If you get off, they could, technically, charge you for a flight to Amsterdam.
Nor do they have to keep you on those flights. Since the OP has booked a flight to Brussels, the airline is obligated to get him to Brussels. What if his flight is oversold? The airline could move him to another flight, even with another airline, as long as they get him to Brussels in a reasonable amount of time. That new flight may not even go to Amsterdam. It doesn't matter where he changes because he bought a ticket to Brussels.
Not showing up for the second part of a connecting fight will cancel the rest of the tickets--including any return flights--without compensation to the passenger.