The Absurd Claim of the Metric as a Tensor

I see that the discussion of whether the metric qualifies as a tensor
or not has splintered into many different localized groups which are
very confusing.  Thus, I would like to put everything into a nutshell
of the pros and cons.  Although the tensors can cover more ranks, the
discussion should only be limited what GR covers.  That is rank 2
tensors or the 4-by-4 matrices.

The definition of a tensor as agreed by almost everyone says that any
matrix invariant under a coordinate transformation is a tensor while
the elements to the matrix can change under the same transformation.