Why does John Travolta play a woman?

John Waters, who wrote and directed the original film had this to say:
(from the article Waters recalls men who played Edna)

In the beginning, Divine played the role of Edna Turnblad. And the first day on the set of “Hairspray,” I didn’t recognize him. I thought it was another neighborhood woman watching the shoot. We were filming in East Baltimore, and all the housewives were talking to him.

Divine looked normal, not weird. It was a moment of truth. It was so anti-the-Divine-character that we started with. Divine said, “Nobody can call me a drag queen, because what drag queen would allow themselves to look like this?”

If there’s a template, that’s it for everybody who has played the role of Edna. And they’ve all taken that to heart. Edna Turnblad isn’t a drag-queen part.

It has become a tradition for men to play her, as with Peter Pan, where it is always played by a woman. Why, I don’t know. It gives it an edge. It’s all about outsiders.

Divine played Edna realistically. The movie I made was actually realistic.

Neil Meron, who produced the 2007 film version (with John Travolta in the role) said:

We hired an actor to play the role of Edna, not an actor to be a man wearing a dress and a fat suit.

John Waters never conceived of the role as a drag role. I mean, it happened to be that Divine was a drag queen, but it's not a drag-queen role. The only tradition is that a man play the role of Edna.