Arching my back is one of my biggest flaws...It's pretty defensive and improper riding.
If you're taking your horse over fences, he should be broke enough to know the aids to stop, so having a more effective core and leg will benefit you more than arching your back. Besides, if you get into the habit of doing it, you're going to have to break that later.
Your trainer is incorrect; a straight back with a good rotational pelvis is correct for any horse or discipline. Arching is fashionable in some barns, but it will not win in the ring and it is completely ineffective. Posted via Mobile Device
Some shows maybe, but it's a big fault. Kind of like how evading the bit and overflexing can win some dressage shows. Just because it wins some places doesn't mean it's correct. Posted via Mobile Device
By chance is the instructor at the same barn where you were ranting about kids jumping with no business doing so on the English riding forum? I'm not even sure why you'd even like to learn from a barn that works that way. Like others have already said, arching your back does nothing but give you a sore back. I don't get where that came from. Flat back when jumping.
Are you slouching? If that is the case then your trainer might be telling you to arch your back so you have a straighter back? I don't think it's the best way to word it but I could see how it could work.