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Why is it wrong to use the concept of hybridization for transition metal complexes?

I have asked a lot of questions on coordination chemistry here before and I have gone through a lot others here as well. Students, including me, attempt to answer those questions using the concept of hybridization because that's what we are taught in class and of course it's easier and more intuitive than crystal field theory/molecular orbital theory. But almost all of the times that I attempted to use the concept of hybridization to explain bonding, somebody comes up and tells that it's wrong.

How do you determine the hybridisation state of a coordinate complex?

This is a link to one such question and the first thing that the person who answered it says: "Again, I feel a bit like a broken record. You should not use hybridization to describe transition metal complexes."

I need to know:

  • Why is it wrong? Is it wrong because it's oversimplified?
  • Why does it work well while explaining bonding in other compounds?
  • What goes wrong in the case of transition metals?