der Gegner
opponent
A person or team that you compete against in a game, contest, or debate.
Im Finale traf sie auf eine starke Gegnerin.
In the final, she faced a strong opponent.

opponent
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opponent
A person or team that you compete against in a game, contest, or debate.
Im Finale traf sie auf eine starke Gegnerin.
In the final, she faced a strong opponent.

The word 'Gegner' (opponent) is derived from the preposition 'gegen' (against). An opponent is therefore literally a person who is 'gegen' (against) someone or something.
Sie kämpft gegen eine starke Gegnerin.
She is fighting against a strong opponent.
The context makes the difference: in the areas of sports, games, or competition, a 'Gegner' (opponent) is a competitor. In politics or serious conflicts, a 'Gegner' (opponent/adversary) is an adversary with opposing goals.
Der Schachspieler analysierte die Züge seines Gegners.
The chess player analyzed his opponent's moves.
In sports and game contexts, 'Gegner' (opponent) is often combined with adjectives such as 'stark' (strong), 'schwach' (weak), 'fair' (fair), or 'gefährlich' (dangerous).
Obwohl es ein harter Wettkampf war, blieb sein Gegner immer fair.
Although it was a tough competition, his opponent always remained fair.
fan
'der Fan' and 'der Gegner' can both appear in situations where people have a clear attitude toward a person, a team, or an idea. A fan supports something or someone and is enthusiastic about it. An opponent is against it, for example in a game, a debate, or an argument about an idea. So the contrast is: the fan is in favor, the opponent is against. This is especially easy to see in sports: fans cheer for a team, while opponents play against it.

Im Finale war der Gegner sehr stark.
In the final, the opponent was very strong.
Mein Bruder ist ein großer Fan von dieser Band.
My brother is a big fan of this band.