How did cougar come to mean predatory woman?

The slang term certainly goes back to 2002. That's the publication date of Valerie Gibson's Cougar: A Guide for Older Women Dating Younger Men.

An item titled "It's a Jungle Out There," in Against the Grain (2002) [combined snippets] attributes coinage of the term to Gibson herself:

With five marriages under her belt, Valerie Gibson is an expert on failed relationships. She is also a self-described "Cougar," her term for older women who date younger men. ("Pumas" are younger women dating older men—really, I'm not making this up.) "It's all about being confident, sexy, and absolutely uninterested in commitment or children," says the New York Post, describing Gibson's new book: Cougar: A Guide for Older Women Dating Younger Men. The book contains such invaluable advice as carry condoms in your purse, try not to have more than three martinis on a first date , think short term, and dress sexy. For older women who have managed to date for years without this information, Cougar is a must-read.

It also seems noteworthy that Gibson's book appears in Canadian Books in Print (2003) and that Gibson is Canadian. The attribution of the term to a Canadian website ("Cougardate.com") may explain where Gibson got the term, or it may indicate that the website adopted its name after having encountered Gibson's book. I couldn't tell from a brief (and yet too long) visit to the website how long ago it was launched.

Victoria Phillips, Confessions of a Scottsdale Cougar (2009) offers this anecdotal commentary on the term's origin:

The slang term "COUGAR" that refers to the older women who date younger men seems to have its origin in a dating Web site that featured mature women hooking up with younger men, founded by two women who were told by their nephew that the two ladies were like cougars in search of defenseless small animals and picked up the term from his mates on his hockey team. So it is figured that the term first emerged sometime in 1999.

Phillips doesn't provide any documentation to support this claimed origin, but the hockey angle is certainly consistent with the asserted Canadian origin theory mentioned by both Wikipedia and Etymology Online.

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Site participant njuffa notes in a comment beneath this answer that the Internet Archive's Wayback Machine finds a webpage for CougarDate dated February 20, 2001, with a page copyright date of 2000. The page includes a brief statement of purpose ("A fun new approach to dating where women are Cougars and men are Willing Prey.") and a link (inactive) to a "cougar manifesto" that would undoubtedly have shed light on the characteristics of the "Willing Prey" of particular interest to members of "the Cougar Den." It follows that CougarDate is slightly older than Valerie Gibson's Cougar book, although the connection between the two (if any) remains undocumented. My thanks to njuffa for uncovering this information.