Refactors so the failing happens in a new public method.

• fixes Allow customizing fail message for invalid choice in click.types.Choice #2621

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• Add tests that demonstrate the correct behavior of the change. Tests should fail without the change.
• Add or update relevant docs, in the docs folder and in code.
• Add an entry in CHANGES.rst summarizing the change and linking to the issue.
• Add .. versionchanged:: entries in any relevant code docs.
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• Run pytest and tox, no tests failed.