The problem is with your sharpening technique, not with stainless steel. Carbon steel is more forgiving of mistakes. It makes everybody seem like a sharpening genius.
Burrs form when you remove more than the minimum amount of material to reach an edge. The burr is the remnant of the material that you thought you removed from the apex of your edge, but in reality it folded away from your hone as you worked. Even with a light touch you can get some burr, but using excessive honing pressure (particularly on a narrow honing surface like a ceramic rod) will cause a larger fraction of the edge to bend out of alignment. So first of all use light pressure as you approach the end of your honing process. Another thing that maximizes a burr is honing on one side at a time. As you get to the later phases of your honing be sure that you are honing on alternate sides of the edge on every stroke (left-side, right-side, left-side, right-side...).
A burr forms because your hone's abrasive particles are not shaving off little bits of the edge like a razor blade. The particles varie from rounded, to pointy, to flat-topped. They shave off some material, but they also have a tendency to simply plow through and bend over some of the blade material. If the blade is extremely brittle like glass it will microchip as you hone it. If the blade material is softer it will not chip, but it will tend to do some burr formation as soon as your edge gets thin. If your carbon steel knife is 58 or 60 RC hardness it will form a bit less burr than a stainless steel blade that is 56 or 58 RC. If your stainless steel has large chromium carbide grains in it those will tend to fold over rather than get cut.
The sure way to debur an edge is to lightly hone edge-forwards at an angle that is significantly greater than your normal honing angle using an abrasive that cuts more than simply polishing. When I do most of my honing at 15 degrees I will bebur using clean medium-grit ceramic rods at 25 degrees. It only takes about 8 light strokes to do it (left, right, left, right, left, right, left, right). Then I go back to 15 degrees and restore my edge with a minimum number of strokes. If you go back and hone too much you will just create another burr.
You may actually still have a burr on your carbon steel blades. Carbon steel is easy to push into alignment and it forms a fairly sturdy burr. For years I happily used burred carbon steel blades. They shaved great and I didn't notice that they dulled faster than they should have. For a kitchen knife you might be happy if you just pushed your burrs into alignment by a little light stroking on smooth ceramic rods or on a smooth steel. You could do the same thing if you sort of lightly hone a burred edge on the side of a glass. Remember to work on a soft cutting board in the kitchen.