Do we move at the speed of light relative to light?

When we say that object A is moving at speed v relative to an object B it means that there is a reference from where B is at rest and A is moving at speed v in that reference frame.

If A is a photon then it moves at the speed of light c in all reference frames so if B is is us then in our reference frame it is moving at c, so it makes sense to say that the photon moves at speed c relative to us, but is it OK to say it the other way round?

If A and B are both objects that have mass so that they move at less than the speed of light, and if A is moving at speed v relative to an object B then in the frame where A is at rest B will be moving at speed v relative to A in the opposite direction. So for speeds less than the speed of light, the speed of A relative to B equals the speed pf B relative to A.

It is tempting to extrapolate this to the case where A is a photon and conclude that therefore B (us) is also moving at speed c relative to the photon. However this would mean that we were moving at speed c in a reference frame where the photon is at rest. This is not possible because we cannot move at speed c in any reference frame and a photon cannot be at rest in any reference frame.

So the answer is "no", it is not correct to say that we move at speed c relative to the photon.