A serrated edge has blunt points that penetrate into the fibers and wedge between the cell boundaries, separating them by tearing, like tiny splitting mauls. They aren't cutting.
I think this is what DocNightfall was talking about. As I read him, he wants to know why everybody's got blunt points on their serrated edges, and why everybody says they can't be sharpened.
If I'm answering the right question here... it's not that it
can't be done, it's just not as easy. A serrated edge takes more specialized equipment to sharpen than a plain one. Notice I said more equipment, not more skill.
To sharpen serrations, you have to have an abrasive, whether that's a natural stone, aritificial stone, sandpaper, or whatever, that can remove metal from that tight interior radius. A plain edge you can sharpen on just about anything. Like the bottom of a coffee cup. But a serrated edge needs gear.
Since most people don't own that gear, most people end up with "blunt points" on their serrations. This is common, but it's not necessary.
It's perfectly possible to have serrated edges that are just as sharp as any plain edge, at every point along the edge... it just takes the right tools.
So to get back to the original question, it's quite possible to push cut whatever you want with a serrated knife, if it's sharp. I have a Vic One-Hand Trekker in my pocket right now. I just push-cut a post-it note, to make sure I could do it, before I typed this. Easy.
So, "it can't be sharpened as keenly as a plain edge" =
false.
"...in general, a serrated edge is poorly suited to push-cutting." This, however, is not necesarily false. I said above that it's no problem to get a serrated knife sharp enough to cut, say, a post-it note. However, I think what you may be reading is people alluding to the fact that it's awkward to do some particular
types of push-cutting with serrated blades, like peeling an apple. The awkwardness doesn't have anything to do with sharpness or dullnes, but with the points digging too deep and the troughs not deep enough. Same with whittling. If you want a smooth and even cut, the serrations will prevent it.
Trickier to sharpen, yes.
Can't be sharpened as well, no.
No good for push-cuts, maybe.
Mike