Quick answer
A hot man manufactures conflict; a patient one quiets it. Both are doing something active, which is why the calm person in a room is never merely passive.
Read both lines
This verse is 15:1 written as a character study rather than a technique. The "wrathful man" is literally a man of wrath, the same word the soft answer turned away in verse 1, so the chapter has moved from the answer to the person who habitually needs one. The second line uses an idiom worth noticing: "slow to anger" is the phrase the LORD uses of Himself at Sinai, rendered "longsuffering" there, which means the patient man in this proverb is doing something God-shaped rather than merely keeping his temper. And "allays" is an active verb. He is not absent from the conflict; he is quieting it, which takes more strength than starting one ever did.
Related: Proverbs 15:1 · Proverbs 16:32 · James 1:19–20
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.