This is a linkpost for https://atheistkit.wordpress.com/2016/12/20/on-truth-on-god-and-on-faith/
I think you are mistaken about this. Not wanting to change to some other word is not because they do not want to admit they were wrong. It is because they do not want to abandon their tribe. By telling them that they should not use that word, you are telling them that they should abandon it.
That's wrong. You should tell them they can use the word "God" for anything they like, and still believe the truth, without having to abandon their tribe.
I think Viliam is right.
Maybe there are some who need coddling, but that's a question of strategy, not clear thinking. If we're aiming for clarity, then what each personally should personally aim for is to just admit when they're wrong and abandon any dishonest comforts like calling God "the spirit within all of humanity."