Why is this an ambiguous MRO?

To be "consistent" the MRO should satisfy these constraints:

  1. If a class inherits from multiple superclasses, the ones it lists earlier in the superclass list should come earlier in the MRO than the ones it lists later.
  2. Every class in the MRO should come before any of its superclasses.

Your proposed hierarchy does not have any possible ordering meeting these constraints. Because Third is defined to inherit from First before Second, First should come before Second in the MRO. But because Second inherits from First, Second should come before First in the MRO. This contradiction cannot be reconciled.

You can read more about the precise method Python uses to compute the MRO, which is called the C3 linearization algorithm.