You seem to be confused. Burrs are bad and give you edges that fold over. Think of it as turning your edge into aluminum foil. Once you do that it tends to flop over from side to side rather than cut off unless you attack the burr with extreme prejudice.
Burrs form when you hone off a lot of material, particularly at low angles or when you work one side of the edge at a time. Often experts recommend that you work one side of the blade until you form a burr then work the other side. This is good advice for people who tend to hone too little and quit before they actually start to form an edge. Unfortunately this can be bad advice for more determined honers who remove more than the minimum amount needed to create an edge. These honers will get rather large burrs that will require extra attention to remove.
Once you have roughly sharpened your blade and create a burr you need to get rid of it. Only certain lucky combinations of steel, strops, abrassive compounds, and techniques will remove burrs via stropping. It is much more common for stropping to simply bend a weak burr into a flimsy state of allignment rather than removing the burr.
It is most reliable to remove the burr via edge-forwards honing on a reasonably agressive hone. I like to use a fine diamond hone, but a medium fine aluminum oxide bench hone works well. If you created your edge by honing at 20 degrees per side remove burrs by light edge-forwards honing strokes at 40 or 45 degrees per side. Only do about 5 to 10 light strokes per side (and alternate strokes left-side, right-side, left-side, right-side). You are sort of dulling the edge (making it more obtuse) at this point so you only want to do enough strokes to remove all trace of burr.
Once you have removed the burr, restore your edge by a minimal number of edge-forwards honing strokes back at your normal honing angle (say 20 degrees per side). By "minimal number" of strokes I mean about the same number of strokes and the same amount of light pressure that you used in your deburring step. At this point your edge should cut paper well. If it doesn't there could be a couple problems. One is that your blade bevel is too steep (thick blade and/or narrow bevel). The steep wedge formed by this blade geometry has trouble fitting into the cut made in the paper. It can help to reprofile this type of blade to a thinner bevel angle (this takes a lot of time). The second possible paper cutting problem is that the blade alloy is hard to work with and you did not really get as fine an edge as you thought in the first place. This can easily happen on ATS-34 or 440C. On some of these alloys a diamond hone would make it easier to really get that fine edge.
Once you have a fine, burr-free edge it may be ok to strop. I say "may be" since some stainless alloys don't seem to like stropping very much. Some of the harder stainless alloys seem to get duller if I strop them much, even with a very good edge to start with. I often do just a little stropping on plain leather with these alloys or none at all. Commonly I finish these with a few strokes on a ceramic rod v-style sharpening setup like a Spyderco Sharpmaker. I like the edge that I get from the ceramic better than I like the edge that I get on stainless when I strop. Plain carbon steels seem to always like strops, but stainless is much more uncertain.
