Why is the Earth not in tidal lock with the moon?

The gravity of the Earth has tidally locked the moon so that the same side always faces the Earth but the opposite has not happened. This is presumably due to a difference in mass.
Question. If the Earth is still spinning shouldn’t the moon also be spinning albeit proportionally slower?

The earth has far more rotating inertia than the moon. Mass moment of inertia for a sphere is proportional to the fourth power of diameter; the earth is 3.66 times the diameter of the moon, so it has 180 times as much rotating inertia. The earth is slowing down…but it’s gonna take a while.

Thw Moon does rotate. See Wiki:

Tidal Lock

You answered your own question - it’s mass.

The result of the Earth / Moon rotation are 2 tidal bulges - one on the side of the Earth facing the moon, and one on the opposite side of the Earth. The gravity of the moon tugs on these bulges and is very gradually slowing down our rotation. That rotational energy is transferred to the moon and is causing it to speed up gradually which is making it move farther away from us - at a speed of just under 2 inches per year.

Yes, but shouldn’t the moon be spinning, just really, really slowly.

If the moon were a blob of viscous liquid with no tensile/shear strength at all, then yes, theoretically you could model its rotational speed as a simple exponential decay, with its rotational speed asymptotically approaching zero.

But it’s not. It’s made of materials that do have some tensile/shear strength, and can’t be modeled as a simple viscous liquid. At some point the rotational speed/inertia of the moon was low enough that it could no longer overcome the structural integrity of the moon’s materials, and it pretty much locked into place.

See reply #3 and go to the link.

It is, with a period of ~28 days. Which just happens to be the period of its orbit too.

Here’s a reasonable article on the change in Earth’s rotation over long geological history. It makes the point I’ve seen elsewhere that by the time the Earth is approaching tidal lock, the Sun will be expanding into a red giant. And that will mess up everything. (Especially when the Sun’s diameter is larger than the current diameter of Earth’s orbit!)

Tidal lock: it’s taking longer than we thought.