I was prepping some .308 brass of mixed types. I had one that the CCI br-2 primer did not want to go in. No big deal, set that one to the side and moved on. Had a total of four that did not want to let the primer press in. All four were Hornady brass. Everything else was Winchester or Federal. I checked the pocket size and the Hornady was .003 smaller than the others. Has anyone else seen this, or were these just a fluke? Seemed funny that only Hornady had the issue.

Every time I've seen it it's always a benchrest primer. Course I've seen it a grand total of 5 times. Not the answer you wanted deadeyes but that's my experience.

Cut the primer pocket out. Problem solved

Haven't used a lot of Hornady brass but Norma and Nosier belted magnum brass has very tight primer pockets. I've started using a primer pocket uniforming tool on all new Norma and Nosier brass because of this and it helps a little.

I have a drill mounted in a vise on my workbench. Anytime a primer pocket is tight or has military crimp I insert case into drill, tighten lightly, spin and use my deburring tool to ream out pocket. Never liked crushing primers before, definitely not going to do it now.

I had a mixed lot of 9mm and almost all the hornady wouldn’t take a primer . I put them through my rcbs swagger and they were good to go

My Lyman case prep center cuts pockets just right.

I think hornady crimps some of the primer pockets on 308 ammo. I have run into that as well and running them through my decrimping die fixes the problem. It's the same if you get Lake City brass for a 223. Sometimes the primer will go right in, but if it won't, then a decrimp is all it takes and then you are golden.

First mistake is using Hornady brass

That’s my approach.
After depriming, cleaning, sizing, and length trimming…I install primers with a hand primer. Most of the time a little wiggle and it slides in. But if not, i swag the primer pocket.