There was a combination of factors. I suggest reading the book "On A Clear Day You Can See General Motors" for some starting information. But for some information upfront, in the 1950s GM had become the largest automotive company in the world, buying makes from all over the world with the money they made from their contracts with the U.S. government during World War II and the subsequent money from their core U.S. divisions within the Sloan Ladder. GM had seen Volkswagen as a threat, but only Volkswagen thanks to their quick proliferation during the 1950s at the lower end of the market. To them the French were essentially making toys, the Spanish would never make anything worthwhile under Franco, the Italians had already gained a reputation for extremely fragile and temperamental cars, and the Japanese were producing enclosed golf carts. Only the British and the Germans were a threat, but by the mid 1960s British automotive manufacturing was nosediving, and German cars were still divided into economy and ultra luxury with almost nothing in between thanks to slow post war recovery and targeting the U.S. upscale market.
During the 1950s the U.S. had invested huge amounts of money into Japanese manufacturing in order to have a cheap place to outsource labor to, and as a good will gesture after what happened during World War II. The Japanese, taking technology from American manufacturers, started making their own advancements. By the late 1960s they were on-par with the Americans in ingenuity, but lacking in quality. This applied to everything from their radios to their cars. At the same time, the Japanese yen was inflated compared to the dollar, making it a good idea to export Japanese goods to the U.S. so that Japanese companies could then trade in U.S. dollars internationally. The goods were cheaper to manufacture and import, and it made companies like Matsushita and JVC quite a lot of money they'd use in the 1970s. Toyota and Nissan were also picking up on this, selling the Toyota Crown and Corona in the U.S. as lower cost luxury options and the Nissan Bluebird (as the Datsun 510) as a cheaper alternative to European sports sedans.
In the U.S., by 1965, GM had a majority control of every market. They had done this by essentially siloing every division and making them work on their own, with their own funds, with no collaboration between divisions without executive permission. Permission which was often not granted. This worked fine for the European and Australian divisions like Vauxhall and Holden, but it was starting to strain the U.S. divisions. Then in 1968 three disasters occurred simultaneously for GM. Semon "Bunkie" Knudsen defected to Ford. Chrysler began courting Mitsubishi for captive imports of cheaper Japanese cars. And Lee Iaccocca perfected the personal luxury coupe with the upcoming 1970 Ford LTD and Lincoln Continental Mark IV, the dominant car template of the 1970s.
In 1973 you had a massive recession thanks the the 1973 OPEC Crisis and the 1973 Stock Market crash. These new huge vehicles that Iaccocca had gotten the U.S. addicted to were suddenly much more expensive to buy and run thanks to being opulent and thirsty. Ford was not immune to this, despite the success of the Lincoln Continental and Mercury Grand Marquis. This worked in Chrysler's favor however, as they had both the Dart in the wings and their captive Mitsubishis. Chevrolet meanwhile had blown public trust with the Vega in 1970 thanks to it rusting on the dealer's lots and destroying it's engine within the first month of ownership. Then once again they took a hit with the 1971 Pontiacs and Buicks, both of which were poorly received due to polarizing styling and issues like the trunks filling with water thanks to a ventilation engineering oversight. Chrysler had misread the market with their 1968 styling, and it took costly changes to slowly update the body dies to be in line with industry styling by 1973.
This primed the Japanese manufacturers to swoop in and take over. Datsun struck first, with the B210 and the 720 taking spots in the economy car and mini truck markets that the Big Three had ignored. Honda hit next with the Civic CVCC, capitalizing on the 1973 OPEC Crisis to provide a fuel efficient vehicle to panicking Americans who weren't satisfied with the disappointing Ford Pinto and Dodge/Plymouth Aspen/Volare twins. Toyota came in last, but strongest, introducing the third generation Corolla and reworking the Celica slightly for 1976 to fit American tastes. With the combination of Americans scrambling for smaller and more fuel efficient cars, the weak Japanese yen compared to the dollar, cheaper Japanese manufacturing due to automation, and cheaper Japanese steel thanks to being untreated and of thinner gauge, Japanese cars sold like crazy after 1973 and spread from California all the way to the East Coast.
This of course caused the Big Three to panic. GM tried several times to fix the Vega and it's siblings, only managing to make just as bad a car each time in the Monza and then the Cavalier. The 1980 X cars were a disaster, with the Chevrolet Citation and it's sisters driving customers away from GM for life. The failed 1985 downsizing of the full sized cars under Ed Cole's direction left every division's cars looking like clones of eachother both inside and out. And finally the dilution of the Oldsmobile brand by naming every car Cutlass killed their last golden goose. The GM10 "W-body" cars, meant to come out by the 1984 model year and engineered to the standards of the 1980 Honda Civic, ended up five years and hundreds of millions of dollars over budget when they arrived in 1988 as 1989 model years.
Ford disregarded the 1970s oil crises almost entirely, continuing to bank on large personal luxury coupes to keep them afloat. A token gesture was placing the Mustang on the Pinto platform for 1974 and playing it up as a baby Thunderbird rather than the performance heavy brute it was in the 1960s. By 1978 these tactics had nearly bankrupted the company, forcing a scramble to the Fox platform as they quickly downsized everything and killed vaunted nameplates to scrub any ill will from the brand. Were it not for the continued sales of the Lincoln Continental Mark V and the development of the Tempo and American Escort, Ford might've followed the path of AMC in the 1980s.
Chrysler was... Chrysler. They were up and down like a spring as they had always been. They suffered through 1973, suffered the failure of the Aspen and Volare, suffered the death of their profit ensuring muscle cars due to rising insurance costs and the fuel crisis, and suffered having to sell an ailing Rootes Group and essentially leaving the European market. But before they sold the Rootes Group they filched a rather interesting piece of technology in the Talbot Horizon. A car which they reverse engineered into the Dodge Omni, the basis of the K-Cars that Lee Iaccocca would champion and eventually pervert throughout his stay at Chrysler during the 1980s. As such Chrysler was the best positioned to survive the 1980s.
But then we come back to Europe. To the already small, fuel efficient, high quality cars that GM had thought no threat in the 1960s. If, during the 1970s, GM had brought over vehicles such as the Opel Rekord and Vauxhall Astra, they would never have had to waste money developing the Vega, the Monza, and the Cavalier. The cars already fit the market GM was targeting. The same was true of Ford. If Ford had brought over the Ford Escort, Taunus, and Granada, they wouldn't have had any need to develop the Pinto, Tempo, and Fairmont. Detroit was too insular and xenophobic to take the option that would have saved them. An option they would inevitably end up adopting thirty five years later anyways.
Detroit died for a number of reasons. But the main reason was the pride of Ford and GM.