Prove that judging others has always been used as judging out of condemnation.
Showing someone they are wrong about something clearly is judgement. You're picking nits.
I'll leave you with some Scripture.
"The mouth of the righteous speaketh wisdom, and his tongue talketh of judgment." (Psa. 37:30)
"The way of peace they know not; and there is no judgment in their goings: they have made them crooked paths: whosoever goeth therein shall not know peace." (Isa. 59:8)
"Dare any of you, having a matter against another, go to law before the unjust, and not before the saints? Do ye not know that the saints shall judge the world? and if the world shall be judged by you, are ye unworthy to judge the smallest matters? Know ye not that we shall judge angels? how much more things that pertain to this life? If then ye have judgments of things pertaining to this life, set them to judge who are least esteemed in the church. I speak to your shame. Is it so, that there is not a wise man among you? no, not one that shall be able to judge between his brethren?" (I Cor. 6:1-5)
"I know thy works, and thy labour, and thy patience, and how thou canst not bear them which are evil: and thou hast tried them which say they are apostles, and are not, and hast found them liars" (Rev. 2:2) How can someone be found to be a liar without judging?