You are absolutely correct, backward facing seats are safer.
But tradition and a subjective feeling of being treated better means that people will prefer to be seated facing forward. Some even claim that they develop motion sickness when sitting backwards. This can indeed be the case for some people in trains with their big windows, but much less so in aircraft.
Just note which seats will be occupied last in a train with lounge/mixed seating.
In order to cram the highest number of passengers into their planes, the airlines would need to convert all seats to the backward orientation, and you can be sure there will be some passengers who will complain. If passenger safety would be important to them, airlines could already use better seatbelts, like the 5-point-harnesses used in gliders and aerobatics planes, but they all use the minimum lap belt which is mandated and nothing more. Convenience and cost always win over safety.
Now I need to mention two caveats:
- If passengers should be seated backwards, the industry needs to develop new seats. It will not be helpful to turn existing seats around - they would collapse at much lower loads than what a backward-sitting human can sustain. However, to fully support these higher loads, seats will be more heavy and possibly even the floor structure needs to be beefed up.
- Backward-facing seating will only help in the fraction of cases where deceleration loads are too high for a forward-facing person, but low enough to make the crash survivable. If the plane flies into a mountain or ditches and sinks before people get out, the better seating will not help.
Some military transports have backward-facing seats. In some crashes, the survivability rate was seven times higher in those than in forward-facing seats. Early air travel also used mixed seating, e.g. on the Zeppelins or the Dornier Do-X. One airline to use mixed seating was Southwest Airlines with their "love seats", and business jets have mixed seating as standard. Thanks to @reirab for pointing out that United Business class also has some backward-facing seats.
Cabin of the Do-X. No seatbelts, seats not bolted to the floor. These were the days ...
Cabin of the Dassault Falcon 7X business jet.