Based on the classical earthly-branch relations of your two zodiac animals — this combination may emphasize these tendencies; real people add the nuance.
Clash pairing — opposites in direct opposition
Rabbit and Rooster sit directly opposite each other on the zodiac wheel — the six-clash (Chong), the most confrontational relation in the system. Values collide fast and arguments start early. Tradition does not forbid the match; it warns that it only works with real distance or deliberate structure.
Best as a working rivalry or a long-distance romance: respect the gap, and the clash becomes complementary rather than destructive.