1

If I make a non-random choice between two options and I claim my choice doesn't make a difference to the outcome, is this a logical fallacy?

Or is it merely a lie in order to hide the underlying opinion which has lead me to the choice?

2

This isn't a fallacy, but rather an example of what Sartre and deBeauvoir identified as "bad faith," which is when a human being denies his or her freely willed agency in the world. That agency manifests in the inescapable necessity of making choices.

Bad faith (from French mauvaise foi) is a philosophical concept used by existentialist philosophers Jean-Paul Sartre and Simone de Beauvoir to describe the phenomenon where human beings under pressure from social forces adopt false values and disown their innate freedom hence acting inauthentically. It is closely related to the concepts of self-deception and ressentiment.
https://en.wikipedia.org/wiki/Bad_faith_%28existentialism%29

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