If there is play in the machine, then climb cutting can cause a sudden jerk, and climb cutting will self feed. However, the cutter is still pushing the work away. Looking at your picture, the cutter enters the work almost perpendicular. The forces are pushing the tool away, but since it has nowhere to go, it appears to grab. If the cutter was actually pulling the work toward it, it would dig in. Instead, it rides along the edge.

Try this. Program two identically sized squares, and cut one with a conventional cut, and one with a climb cut. The climb cut will always be slightly larger, because the bit is pushing away from the material. With the conventional cut, the bit is pulling into the material, resulting in a smaller part. A lot of shopbot users use this to their advantage when cutting cabinet parts. They do a "rough" climb cut sluightly oversize, then finish with a conventional cut. By removing a very small amount with the conventional cut, it minimizes the effect of the bit being pulled into the parts.