I wondered that as well. One hypothesis from the article: "according to Lena C. Edlund, a Columbia University economist... One reason young women in the prime marriage years - the 25-44 age range - flock to big cities is to compete for the most eligible men. And smart women who gravitate to vibrant cities are more likely to stay single - for longer, at least - because they rightly refuse to settle for someone who can't keep up with them intellectually or otherwise."

And later, talking about the West: "As numerous studies of migration show, men - especially those in regions with declining economies - are initially more likely to move long distances for economic opportunity, while women are more likely to stay closer to home and family."

Admittedly these explanations don't make complete sense to me, though, and I'm suspicious of the phenomenon in general.

1000 foot view:

East is old culture + institutions, west is new. Think new york + boston vs LA and SF. The east coast was settled long before cities on the west.

In broad strokes, men look to make something new / upend the existing order, and women fit into existing structures. Mirrors the age-old biological reality - men can concieve at any age, with multiple partners. Women have a limited reproductive window and carry the blood cost of reproduction. Women are more stable as caregivers, men are higher variance.

Not to say it all goes down like that, obv social norms change and people can be whatever they want, but the "bare metal" underlying biology has an impact.