When you sharpen a knife to a very thin edge, the thinnest portion at the very edge is so fragile it bends over at almost any pressure when you are trying to cut something. This is known as a burr or a wire edge or a feather. If you are using a blade as a razor, you want an extremely thin edge, but not for ordinary utility cutting.
See: "the secondary bevel, put in a narrow strip at the very edge for extra strength, at a slightly more obtuse angle than the primary"
So what you need to do is to break off that wire so the blade is left sharp but not flexible at the edge. One good way to do this is to sharpen it a few strokes at a more obtuse angle than you've been using, and to strop it. (Sharpening is generally done with the edge moving forwqard, stropping by pulling the edge back.)