A shirt and tie are a bit pretentious. They tend to alienate students from instructors and ground staff from flying staff.
There is a need to be well turned out, but not stuffy. We are teaching people to enjoy their flying. It's supposed to be fun, lets not get above ourselves here. If both you and they are relaxed.... Makes sense really. Smart casual, as has been put before is in my opinion the best way to look smart and be comfortable.
As for needing to wear a tie to put over a sense of professionalism. If you can't do that by your actions and manner, then you are in the wrong business.