The problem here lies in neck tension and the "schmutz" left in the neck of your fired case versus bare virgin brass of the new case. First, the bare brass is probably letting the bullet slide more easily across its surface, where the fired brass with burned carbon and likely some slight galling from the original bullet sitting in there for a period, offers more resistance when seating. Brass and copper are soft materials and soft materials tend to bond easily under pressure. Have you ever tried pulling a bullet from a very old round? If you get the opportunty sometime, do it and then have a look at the inside of the neck.
Run your new brass through your sizing die just as you would a fired case. Brush the necks of the fired case really well before running them through. Debur all and let us know how you make out.
Rooster