Why did Doyle makes Holme’s adversary a female?

We can't be absolutely certain, but perhaps Conan Doyle created Irene Adler because he wanted to provide Holmes with a particularly formidable adversary. In the 19th century, women were expected to be passive, demure, and appreciative of their menfolk. Irene Adler breaks the mold of Victorian womanhood, showing herself to be remarkably resourceful and intelligent, more than able to compete and succeed in a man's world.
Even Holmes, the quintessential chauvinistic male, is suitably impressed, referring to Irene as "the woman." He acknowledges Irene's intellectual superiority and is big enough to admire her, despite the fact that she's so cleverly outsmarted him. Holmes seems able to handle this unprecedented humiliation quite well, because Irene is very much a unique woman; it's highly unlikely that he'll ever encounter another female capable of getting the better of him. That said, the whole episode fundamentally changes Holmes's previously low opinion of women's intelligence. Thanks to the formidable Irene Adler, Watson notices that Holmes no longer speaks disparagingly of the cleverness of women.