The Bible says...

"Judge not, that ye be not judged."
(Matthew 7:1)

This is one of the most misunderstood and misquoted verses in the Bible.

The Bible also says...

"But he that is spiritual judgeth all things..."
(1 Corinthians 2:15)

Do these contradict each other?

No.

In the first verse, the Greek word used for "Judge" means to try (as in legally), convict, or damn. In the second verse, the Greek word used means to investigate.

So this word translated "Judge" is actually two different Greek words.

Big difference.

Because we cannot always see the shortcomings in ourselves, God expects us to tell others what we see in them if we see a problem:

"Iron sharpeneth iron; so a man sharpeneth the countenance of his friend."
(Proverbs 27:17)

So, the "judging" we are expected to do is not condemnation, it is information that can be used by the wise ("A word to the wise...") to make them sharper, if they so desire.