Quoting from a previous answer is just a starting point not intended to discourage more discussion. More questions, info, and debate are welcome.

When

It's a bit of a quibble, since you are interested in "why", but I'm not certain of the end date of behatteddude. I don't know the number of men wearing hats, but I can at least find images dated before then with mixtures of men with hats and men without hats.

• "the 1923 FA Cup final between Bolton and West Ham", http://www.dailymail.co.uk/sport/football/article-2264693/Footballs-Golden-Years-pictures-The-supporters--Wembley-The-Kop-Stretford-End.html . It also has "servicemen at Wembley for a wartime match between England and Scotland in 1943" and "a match between Chelsea and Arsenal at Stamford Bridge in 1947" ... but maybe football [soccer] or sporting matches were an exception to hat etiquette (though I don't remember ever seeing such a rule)
• "Large crowd watching Durham Miners Gala procession past the Royal County Hotel. 28th July 1950." at https://www.flickr.com/photos/beamishmuseum/4786139005
• Joliet, IL some time in the 1950s, http://www.alamy.com/stock-photo-1950s-main-street-small-town-america-intersection-of-chicago-and-cass-100125169.html
• A parade in downtown Detroit in 1951: http://multimedia.detroitnews.com/pix/ae/57/f6/bc/41/18/20131002180039_1951crowd.jpg

But you can certainly find plenty of images with lots of hats, so there's not a lot of point either way.

And Why

There were citations of sources for decline prior to the 1950s in "In the early/mid 20th century did men really wear hats all the time, and if so, did they always have crazy hat hair?" under https://www.reddit.com/r/AskHistorians/comments/469icw/in_the_earlymid_20th_century_did_men_really_wear/d047274/ . That has a link to a couple of articles (Esquire and a contemporary newspaper) that cited surveys of the time, with reasons. The links on the uppermost reply were not curated, so cum grano salis.

'"[J. F.] Kennedy despised how he looked in hats and usually refused to wear them - despite howls of protest from habderdashers whose hat sales took a precipitous downturn in the 1960s" (Barbara Perry). What factors led to the downturn in menswear hat sales in the 1960s?' at https://www.reddit.com/r/AskHistorians/comments/68hta6/j_f_kennedy_despised_how_he_looked_in_hats_and/ has several answers by /u/chocolatepot

In a sibling comment to this, /u/ShaiDorsai mentions the theories that it was Kennedy or Eisenhower what done it. I think that it's desirable to more firmly debunk the Great Man theories here. The decline in the US began before either man. I recall reading that Eisenhower was often enough seen hatless; snopes in "John F. Kennedy’s Hat" at https://www.snopes.com/history/american/jfkhat.asp states "Dwight D. Eisenhower, who frequently went hatless throughout his eight years in office". The only applicable-looking citation is Ambrose, Stephen E., Eisenhower: The President.