I use CCI primers almost exclusively. I use CCI 250's, 200's 450's, 400's, BR2, BR-4, and small/large pistol. So all except precussion caps, 50 bmg, 34's, or 41's
Anyway.
2 things about CCI primers.
1: They are hard, and need a strong spring/pin
2: they are hard, they need to be seated and slightly smashed. I seat to .006 below flush.
But in tens of thousands of CCI primers, I had a batch of 250's that would yield a FTF about every 50 rounds or so. It wasn't the firing pin, or seating depth, but the primers.
But like Unclenick said, if they were left in a storage container at 200 degrees or something for several months....But that is the one and only brick out of tens of thousands of primers I have ever had an issue with. But it does happen.
If you have a different gun, you can rule out the firing pin. You can't check a struck pin that didn't fire to see how deep you set it because it will smash some after a strike, or get seated deeper. So you can measure primer seating depth of all you have loaded , write it down, make each one so you know which is which and see which ones misfire. That would rule out seating depth.
Or you can, much more easily, try a different lot of primers changing nothing else and if they all work, pitch the bad batch....this is the simple solution.