Actually, a piece of paper is great because I do not need to awkwardly unlock my screen to get the boarding pass display; I do not need to worry about an accidental key press switching to somewhere else; if an official needs to actually handle the boarding pass I can hand it over; if the airline rep needs it to change my flight they can do it without having a scanner on every computer. The list is endless.
Also, consider the fact that you have to show the TSA your boarding pass. If you have to unlock your phone for that, they get full access to copy all your data if they decide you look like a terrorist.
Likely not a consideration for most people who don't mind privacy stuff, of course.
Apple's Passbook works from the lock screen without having to unlock the phone itself. The pass shows up when your within close proximity to the airport.
Do we even need an electronic boarding pass? It will not be long before all valid passports are chipped. A security agent or airline staff can just read your passport to verify you are boarding the correct flight. Gate number and flight times often change so it would be unwise to rely on your printed paper for that information. You could be told your seat number by the crew member making the final check at the door of the plane and your initials could be displayed above your sear as a reminder when you near the correct isle.
Don't knock paper too hard. While it's not so good for networked communications, it's awesome for displaying static information, tearing apart, and drawing on with incredible ease (e.g. when you need a picture, text, or information circled in addition to what's printed). It's also very cheap even if it's not free. Paper is also extremely high bandwidth - no waiting to view it. Flipping through a book yields a higher dpi and throughput than the fastest computer displays.
This is not to say that paper is superior for all the uses of a boarding pass, but it's very hard to displace something so usable and accessible to people without smartphones.