Added
The following is how I mentally visualized what I just wrote, earlier, in the Overview. I tried to use words there, but here's the mental picture that was in my mind while I was writing it:
For larger values of \$\omega\$ the reactance of the capacitor has a smaller value and therefore the radius of the above circle is similarly tighter/smaller, and the magnitide is therefore smaller. The differentially-arranged opamp is pushing on \$R\$, which causes the rotation. But no matter how hard it tries, \$R\$ is always positioned to be tangent to the \$C\$-axis, so all the pushing does is to just continue the rotation.
I admit that the \$R\$ and \$C\$ on your schematic was nicely arranged for me to see this circle superimposed on it when I was first reading it. I actually super-imposed the circle, mentally, then. ;)
Added
The following is how I mentally visualized what I just wrote, earlier, in the Overview. I tried to use words there, but here's the mental picture that was in my mind while I was writing it:
For larger values of \$\omega\$ the reactance of the capacitor has a smaller value and therefore the radius of the above circle is similarly tighter/smaller, and the magnitide is therefore smaller. The differentially-arranged opamp is pushing on \$R\$, which causes the rotation. But no matter how hard it tries, \$R\$ is always positioned to be tangent to the \$C\$-axis, so all the pushing does is to just continue the rotation.
I admit that the \$R\$ and \$C\$ on your schematic was nicely arranged for me to see this circle superimposed on it when I was first reading it. I actually super-imposed the circle, mentally, then. ;)