It seems there is one in every crowd. Faye. I haven't yet learned how to ride from behind while I am longing a horse. The purpose of bitting a horse up before riding it for the first time is to introduce it to pressure on it's mouth. Aside from this being a safety measure, when it is the horse that is applying the pressure through it's own resistance it will submit to it much quicker and with less resistance than when a rider is pushing a totally green horse onto the bit with their seat and hands which would be poor horsemanship to say the least. Playing with the corners of a horses mouth to encourage it to lower it's head is not see sawing. It can be accomplished with only the little fingers. I specifically stated that this is nothing but an exercise. Watch the Grand Prix jumping horses. At the end of a course many will lower their nose almost to the ground at the end of a course. They don't just naturally do this. It has been taught to them in order to calm them and to keep them from becoming wired. I haven't been here in a long time. Do you ever offer anything that is positive or do you just lurk and criticize those who make the effort?
If you want your horse to stretch - the first think he must do is 'Accept the contact of the bit' often best taught lunging in appropriate length side reins, the horse worked from behind into the contact - it goes and seeks the bit.
Correctly stretching you should be able to ease the reins or hands forward and keeping the rhythm as the horse stretches into the contact.
All this stems from a rider being able to keep a soft consistant contact on the horses mouth while maintaining forward, controlled impulsion.
Any instructor that wants you to bit up, or use gadgets is not worth working with.
Regardless of what discipline you are aiming for go to a good dressage trainer to get taught the right way to school a horse on the flat.