There'a great old
Soviet book by A. A. Yuryev called "Competetive shooting" that explains this phenomenon really well. It's really an amazing book; if you can find a copy about it, get it. The basics of shooting are the same, no matter if it's 60s in the Soviet Union or 2021 in USA. Also the human instincts and physiology are the same. Calibers and guns change; the human and the challenge remain the same.
When pulling the trigger, there are two things happening simultaniously in your nerve system. You want to pull the trigger because you try to hit that bull's eye. You know how to do it; you've practiced; your muscles are trained for that. Your brain tells your finger to do it. On the other hand, you don't want to do that; you know you will feel a nasty kick and hear a very loud noise. Your brain tells your finger NOT to do it.
No matter how tough a guy you are, your nerve system doesn't like being kicked and loud noises. It's like if you're supposed to push a button that gives you an electric shock to your nipples. It's difficult to push that relaxed, nice, easy and softly. Not that I've tried, but...
I'm not a great shooter, but I'm OK and I don't admit I flinch. The largest caliber I normally shoot is .30-06 and all my rifles are suppressed. I've had a failed cartridge that didn't go off and I've had cases where there wasn't a round in the chamber when I thought there was. I didn't flinch. I think it's mostly due to being suppressed. Also, when on the range, I still wear muffs or even double; plugs and muffs. It just makes it even more pleasant and easy. And if it helps me in not developing a flinch, it's even better. I also admit that when shooting prone or from good rest I don't really know when the gun says bang. I increase the pressure on the trigger until it goes off. I'm not sure if this is a good way to shoot, but when it doesn't matter if it's 0.5 second this or that way, it seems to work. When shooting without support it obviously doesn't work as I have to make the shot when the crosshair is where it should. I'm not great at that, to be honest. But I practice...
However, I never see the bullet striking on .30-06. On rimfires (17HMR or 22LR) it happens. Maybe even on 223. But on a light 30-06 the recoil throws the gun enough to prevent me from seeing what happens. Many here say one should always be able to see the bullet hitting, but that doesn't seem to happen to me. Don't know if I just suck or if this doesn't apply to light guns.