I have had this problem with a variety of horses over the years. Most recently the horse with the problem had an ulcer so I’d encourage you to get that checked. One horse needed his sternum adjusted. Some horses are just very sensitive. Try starting the girthing process from the left (near) side and then do the tightening from the right (off) side. There is a major nerve on the left that on some horses is more sensitive. Also, consider trying a wider girth to spread the pressure out and/or a girth that has some “give”. I find that many people girth their saddles too tightly. You should be able to put your hand under the girth at the sternum (midline).