
das Gegenteil
opposite
Something that is completely opposed to another thing in its qualities or meaning.
Hass ist das Gegenteil von Liebe.
Hate is the opposite of love.
opposite
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opposite
Something that is completely opposed to another thing in its qualities or meaning.
Hass ist das Gegenteil von Liebe.
Hate is the opposite of love.

on the contrary
A fixed expression used to negate a previous statement and emphasize that the opposite is the case.
Ich bin nicht böse auf dich – im Gegenteil, ich bin froh, dass du ehrlich warst.
I'm not angry with you — on the contrary, I'm glad you were honest.
The word is made up of 'gegen' (against) and 'Teil' (part). So it literally describes the 'part' that stands opposed to something.
Das Gegenteil von „heiß“ ist „kalt“.
The opposite of 'heiß' (hot) is 'kalt' (cold).
When 'Gegenteil' (opposite) has the meaning 'opposite thing', it is almost always used with the preposition 'von' and the dative to name the reference point.
Sein Verhalten war das genaue Gegenteil von dem, was er versprochen hatte.
His behavior was the exact opposite of what he had promised.
The fixed expression 'im Gegenteil' (on the contrary) often appears at the beginning of a sentence to correct a previous statement. In this position, it introduces a main clause and requires inversion (the verb comes directly after it in position 2).
Er ist nicht faul. Im Gegenteil, er arbeitet mehr als alle anderen.
He is not lazy. On the contrary, he works more than everyone else.
opposite / contrast
Both words refer to something opposite. „Das Gegenteil“ usually refers to the opposing thing or quality, while „der Gegensatz“ more often refers to the relationship or comparison between two sides. Use „Gegenteil“ for a single opposing position and „Gegensatz“ for the contrast between both sides.

Das Gegenteil von warm ist kalt.
The opposite of warm is cold.
Zwischen den warmen und kalten Farben besteht ein deutlicher Gegensatz.
There is a clear contrast between warm and cool colors.