In the past, dry firing was an important part of firearms training. Target shooters did it, military recruits did it, and so on. If you look around you'll find dry firing recommended in many shooting instructions by top shooters throughout the 20th century to today. We did it in the Navy when learning to shoot the 1911.
Any machine that is used can eventually show wear. From motorcycle engines to electric can openers. A primer slows down the firing pin somewhat, softening the blow. Or actually, ensuring the firing pin stops all the blow - when you dry fire the pin doesn't stop the action, some other hammer block or such does. I'd say breaking a firing pin is most likely if it is hitting live cartridges, not just flying "in air." Wear on the hammer or other parts that are much more robust and might wear, or even be battered or break, after hundreds or thousands of dry fires. But a few times won't hurt. I'd wager MOST old guns we cherish have been dry fired at least a few dozen times. DA revolvers and 1911s that may have been in the military or police: hundreds.
I won't dry fire rimfires, where the parts to prevent the firing pin from hitting the chamber rim are much less robust. Some modern .22s, like High Standards, are known to batter the chamber if the firing pin is slightly long, stretched, worn.