He advocates talking about "breakage" and "accretion" instead of the vague term "change".
His most controversial point, as far as I remember, was that any breaking change (i.e. a major version bump in semver) might as well be considered another product/package/lib and should better choose another name instead of pretending to be the same thing with a bumped number. For me that is taking it too far in most cases (e.g. when the intent of the software remains the same), since it would also have very disruptive effects on the community, documentation, reputation, ... of the package.
Another thought about semver: a bugfix requires only a minor version bump, but IMHO this could also be breaking if people were relying on the buggy behavior. I see the value of semver, but I guess it will always be a too-neat abstraction over something that is inherently too complex to communicate in a simple version string.