As Fred noted above, it's a combination of the limited body taper and the sharp shoulder angle. The case goes into the chamber at a slight angle. Due to the lack of taper there's very little clearance or wiggle room for the case to align and slide in. What's happening is the body-shoulder junction is hitting the top of your chamber while at the same time the bottom side of the body of the case is sliding along the bottom edge of the chamber edge and it basically wedges itself there causing it to stop. When you take forward pressure off the bolt and move it back slightly it takes the tension off the case so it can tip and properly align with the chamber (front tips down/rear comes up) allowing you to then easily push it home and close the bolt.

The feed cone Robinhood referred to is the common solution when the tip of the bullet (usually hollow points) hits the breech face of the barrel just below the chamber and jams things up because of the .223's small diameter. It's the same feed cone that's cut into every M16 barrel that's ever been made for the same reason. Whether it will help in this case really depends on the angle at which the case is at and how far it is into the chamber when it jams up on you.

This is also why most who go to an AI (especially a small diameter AI) make them single-shots - they can be a bit fickle when it comes to feeding from a magazine.