Basil is not and never has been a unisex name. It's a man's name, and in the US it never caught on. It's a very cliched name for an upper-class, early-20th-century British man.
Also, some people say bazzle, some rhyme it with hazel. That ambiguity is a dealbreaker for me by itself.
Before you criticize a man, walk a mile in his shoes. That way, when you criticize him, you're a mile away and you have his shoes!
Steve Martin