Distribution (Dirac&standard) formulations of f=ma... how do they go again?

That is what I mean. I just don't understand how it follows.

[i] If F=dp/dt is just shorthand for three separate equations for each component of force, then F=dp/dt entails that there is nothing special about one particular component. [ii] But there is something special about the component that is parallel to the velocity: there is more inertia in that direction.

This argument against F=dp/dt contains only two premises, [i] and [ii], and is clearly valid. So either [i] or [ii] (or both) is false?