This is the 3120th most frequent German word.
dagegen
"Against it" or "on the other hand."
The word "dagegen" is used here to express opposition to the idea of changing the rules.
Ich bin dagegen, dass wir die Regeln ändern.
I am against changing the rules.
In this sentence, "dagegen" indicates there is no opposition or objection towards liking the color green.
Andere mögen die Farbe Grün, ich habe nichts dagegen.
Others may like the color green; I have nothing against it.
Here, "dagegen" is used to express dissent or disagreement with the passing of the new law.