A word for a person who always criticizes people, and he always claims that he is the righteous.
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Hyper-critical is a good option to describe such a nature. The question has been answered well in another forum for English within Stackexchange. You can have a look: https://english.stackexchange.com/questions/91506/word-for-the-behavior-of-people-who-complain-at-everything-you-do
Probably a "hypercritic" - a person who is excessively or captiously critical
Or "hypercritical" as an adjective.
You could concatenate "constantly ratifying", "self-righteous" and "hypercritic" to call such a person a "constantly ratifying self-righteous hypercritic".