People say a lot things.
The truth of the matter is that perfect truths don't exist. Everything just exists in degrees of more or less wrong, and different systems of judgement we call 'perspectives'.
I completely agree with your implied determinism that some fights/arguments/discussions just aren't worth it. The cost vs benefit just makes some things a pointless affair. And even beyond that, you aren't obligated to lift others' ignorance.
That being said, letting other people win their arguments doesn't mean you have to accept their beliefs. Form your own via more legitimate systems, like philosophy. Moral philosophy has a lot of well thought-out ideas you can use to judge for yourself your own actions and beliefs, and the security of knowing that your reasoning comes from a better place than the haphazard emotional reasoning that most people employ should help you a fair bit to endure.
And even if you do determine with confident certainty that you do do some sh***y things, at least you're certain of it. A rather ambiguous saying that I like to use is that "You can't do what you don't know". If you want to improve, knowing where you stand is imperative to figuring out if you're actually improving or not, much less what direction to take to actually improve yourself.
In any case, certainty breed confidence. And for better or worse, confidence tends to be highly resistant to the pressure of beliefs of others.
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Thank you deeply for sharing your experiences. I don't feel so alone anymore.