Howdy. I loaded up some rounds for a FN Mauser in .338-06 that I just acquired. Upon test firing I had two failures to fire and two hang fires. Upon investigation I found the failures to fire had nice heavy firing pin strikes on them. I then went through the rest of the unfired rounds and found several with primers that were higher than the case head. The brass was brand new Winchester 06 expanded to .338 in a Redding die.
I would suspect the rifle but the previous owner has had no problems with it.

It could be that some of the firing pin's energy is being 'wasted' seating the primer.

You might try gently seating the primers to the bottom of the primer pocket with a handheld priming tool. Keep the bullet pointed in a safe direction while doing so.

George

There was an interesting and thorough article on primers in one of the very recent issues of American Rifleman. If you can get a copy and read it, you'll have a great understanding of them and an explanation of the problem

Briefly, the pellet in the primer needs to be activated for maximum sensitivity. Partially seating a primer gives at best inconsistent ignition and at worst, misfires. The primers are designed to be seated .003"-.005" below the face of the head. Because of the tolerances to which they are built, this enables the anvil to seat into the pellet providing maximum sensitivity. If you'll seat your primers completely and below the face, they will have the sensitivity for which they are designed and your problem should be solved.

All reloading tools are subject to some wear. I've twice found priming tools that did not seat the primer deep deep enough even though maximum force was applied (not a good idea by the way). A new priming pin corrected the problem.

P.S.: Be sure to wear safety glasses.

Don't try to reseat the primers on loaded ammo. It's just not worth it. Pull the bullets, save the powder and start over with new brass.

Some of the new lots of Winchester brass has had very tight primer pockets on the inside diameter.

Go out and buy some Remington brass and use that.

No primer is going to bet set off seating it! The danger would be less than being hit my an asteroid!