Your girth (English) or cinch (Western) needs to be snug enough for you to mount the horse without the saddle slipping to the near side of the horse. I always (30 years+) tighten to adjust and fit 1st, lead to where I am to mount, tighten again, check tack, then tighten a 3rd time before mounting.
I teach my horses to hold their breath, so that it is really snug when I mount, but after schooling, I generally dismount and can get my fist in between the girth and the horse. Positioning is really important.
The girth or cinch needs to be at least 4 fingers width behind the elbow. If you girth is too far forward so is your saddle and THAT could be your horse's discomfort. Some Western saddles--I own one of these--cinches further backwards, and our CW McClellans girth up many inches further back than that.
Sometimes people with sensitive skinned horses will also take the time to pull each leg forward before mounting to make sure that nothing is uncomfortable. http://www.schleese.com/documents/In...%20Problem.pdf
If you ride English, you should tighten higher initially on the off side, then tighten alternately until it is tight. Many English riders use an elastic end girth (that buckles to the billets) to help you get it tight without "cutting the horse in two."
Btw, we all kinda glance through these posts. I want to repeat this: I teach my horses to hold their breath, so that it is really snug when I mount, but after schooling, I generally dismount and I can get my fist in between the girth and the horse.
Hope this helps you. =D