Considering your symptoms, and the fact that it's .223 cal Federal brass, I'm just about certain that you're dealing with brass that was crimped to hold the original primers in place. In order to seat new primers, you'll need to remove the crimp from around the primer pocket.
Here's an example of a piece of ring-crimped brass:
And an uncrimped primer pocket for comparison:
There are several different ways to remove the crimp - if you do a search here or on Google, you'll find all of them.