The second line is genuinely ambiguous in Hebrew, and the NKJV footnotes its key word.
Quick answer
Violent men hate an innocent man simply for being one. What the upright do about it depends on a phrase that can be read two ways.
Read both lines
The first line is clear and unpleasant: the hatred needs no provocation, and blameless is the provocation. A man doing nothing wrong is an accusation to someone who is.
Why translations differ
The second line reads וִישָׁרִים יְבַקְשׁוּ נַפְשׁוֹ, and the NKJV footnotes nephesh as Lit. soul or life. The phrase "seek his life" is the standard Hebrew idiom for seeking to kill someone, which would make the second line say the upright also seek the blameless man's life, an alarming reading. So translators either take nephesh in its softer sense, giving "seek his well-being" as the NKJV does, or read the verb as care for rather than hunt.
This expression is debated and the catalog does not settle it. What the entry rests on is only the first line, which is not in doubt: hatred of the blameless is a real thing, aimed at people who have given no cause.
Related: Proverbs 1:11–19 · Proverbs 29:27 · Proverbs 11:9 · Psalm 37:32
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.