The phrase "cat and dog weathers" is not a single word. However, we can find antonyms for the individual words in this phrase. In terms of weather, the antonym for "cat weather" would be mild or calm weather, while the antonym for "dog weather" would be dry weather. As for the animals themselves, the antonym for "cat" could be "dog," and vice versa. These words represent starkly different characters that have been celebrated and vilified in various cultures. However, it is essential to remember that antonyms are not always diametrically opposed. Instead, they often present a spectrum of possibilities between two extremes.