It's kind of poorly worded. Hitting V1 means you are committed to taking off, single engine failure or not - but you HAVE to reach V2 to safely climb on one engine.
This should happen within moments of hitting Vr, but being single-engine after V1 means you went from hitting Vr halfway down the runway to potentially doing so at the ass-end of your minimum runway length. This means you have basically no room for any pilot error or other failures, and why engine failure on take-off is routinely rehearsed.
Not sure where the original disagreement came from. I never said an aircraft should be able to take off at V1. Perhaps you took the "fly" literally which is fine but that was certainly not the intention.
This should happen within moments of hitting Vr, but being single-engine after V1 means you went from hitting Vr halfway down the runway to potentially doing so at the ass-end of your minimum runway length. This means you have basically no room for any pilot error or other failures, and why engine failure on take-off is routinely rehearsed.