Asymmetric edges aren't weak in general, but they don't stand up to steeling well.
Steeling trues an impact burr by bending it -- with what you called "lateral pressure -- back and forth until the burr is (first) even, (then, second) straightened. In essence, this is the same thing as "chasing" a burr and causes metal fatigue at the crease along which the burr bends. Bending the burr back and forth causes the metal to fatigue. That's a good thing when you're chasing the burr in order to deburr as part of the sharpening process; but a less good thing if all you want to do is true the edge because the metal will tend to break or tear along the crease.
Highly asymmetric edges have inherently acute included angles, which means there's not much metal at that crease, which means that they fatigue -- everything else being equal -- more easily than more symmetric edges. Further, the vector of stress which goes through the blade doesn't travel "straight," but is more complimentary to the sharpening bevel than to the back bevel.
The force applied to the blade when truing is a product of the pressure. That is, unit of mass per unit area. Because rod hones have such small contact patches, the force exerted is much higher than when equal pressure is exerted using a method with a larger contact patch -- such as a strop or bench stone.
But as already said an asymmetric edge is not well suited to repeated bending, and the greater the force, the greater the fatigue. And because the vector of force is not straight across, when the metal does fatigue to the point of breaking the break does not create a fine, narrow edge.
Hope this helps,