Having “bigger fish to fry” means you have more important things to do.
Even though the first known written examples of this expression are over 400 years old, it is fairly certain that the expression is much older than that. One clue is that there are similar expressions in other languages.
For example, the French say, “He has many other dogs to whip.” The Germans say, “I have other hedgehogs to comb.” A similar phrase, “There are other fish in the sea,” dates back to about 1573.
The expression “bigger fish to fry” is attested from the year 1660 in the work titled Memoirs written by John Evelyn. It also appears in the work of the Spanish novelist Miguel de Cervantes in the two volumes of Don Quixote de La Mancha, published in 1605 and 1615, and was translated as “other things on which to think.”
I have read that there are anywhere from 1,600 to 3,500 idioms in regular use in English, with some 130 of them invented by William Shakespeare alone. The reason there are so many is due partly to the use of catchy alliteration and the reference to ordinary, every-day common objects.
Shakespeare was a brilliant writer, but I’m not sure even he could do better than, “I have other hedgehogs to comb.”