Of all the professional sports out there, cricket is probably one of the few where, in theory, a woman should be able to compete at the highest level with men. It's not a sport based on strength or size or speed, all you really need is some decent skills, reflexes and hand-eye coordination. It's very easy to imagine a woman who's a good enough spin/medium pace bowler to bowl against the best male batsmen, while being sufficiently competent at fielding and probably batting down at 10/11...like that's a very feasible goal to aim for. And then you already have Sarah Taylor - an elite level wicketkeeper who is competent enough with the bat to not be an absolute tailender. She's played grade cricket in Australia, and you think with enough training she could be a competent enough wicketkeeper for the men's international cricket.
But I could be wrong. It will be interesting to watch in the next couple of decades if any women emerge who are good enough to prove this theory.
While strength and size and speed are more critical to some other sports, they are certainly an asset in cricket as well. Most batsmen would much rather face a 70 mph bowler than a 90 mph bowler, and the latter is much more likely to be selected for an international side. The proportion of sixes per ball is much higher in mens cricket than womens, probably because of the relative strength of the batsmen.
Also, in the vast majority of competitive activities that require no physical strength but where success is measured purely objectively and not subjectively, the leading practitioners are almost exclusively male. For example:
Chess - The leading women's chess player, Hou Yifan, has been described as "leaps and bounds" ahead of her competitors, but her FIDE rating is lower than the 100th best male player in the world.
Darts - Anastasia Dobromyslova, three times womens world champion, spent three years attempting to compete on the main tour and struggled to break into the top 100 of the world rankings.
Mathematics - In the International Mathematical Olympiad (IMO), only two of the 50 most successful competitors of all time are female. The IMO is the mathematics field most important world event, widely described as the "most prestigious mathematical competitions in the world" and vaguely equal to the Olympics, which is why it's called an Olympiad.
Snooker - Reanne Evans, by far the best womens player ever, won the Ladies World Snooker Championship a record ten successive times between 2005 and 2014 and at one point won 61 consecutive women's matches. She was awarded a wild card on the professional main tour for the 2010–11 season, and failed to win any matches throughout the entire season, suffering 18 consecutive defeats.
Quizzing - In the 15 year history of the World Quizzing Championship, only one woman, Dorjana Širola, has ever finished in the top 10, and she has never been in the top 5.
World richest people - Of the worlds 50 richest people, only five are women, and all of these inherited their wealth.
