There is no constitutional "right to fly". When you purchase a ticket with an airline, you agree to the terms and conditions. This includes the fine print that they may bump you from the flight at any time (prior to takeoff, I assume) for any reason. Commons reasons include overbooking, or if you are judged to be causing an unsafe environment (usually at the captain's discretion, because they have ultimate responsibility for delivering the plane safely to its destination).
If an airline removes you from the flight when you are not causing a disturbance, federal law requires them to either get you to your destination within an hour of your originally scheduled flight. If this cannot be done, they must provide you with a reimbursement of your original ticket, plus an additional amount, which varies depending on the duration of the flight (and delay). Usually this is done by giving a voucher, but passengers are legally entitled to receive a check instead.
Personally, I don't like it, but I realize that the airline has absolute authority over their vehicle. It's nice of the government to at least require them to reimburse you, IMO.