As a resident of Michigan with deep ties to the Detroit area, I can safely say that you will get a different answer to your question depending on who you ask. Like anything in history, there is no one clean cut answer to why Detroit became the way it did. It's a combination of various elements causing the perfect economic storm.
Let me start with the motto of Detroit, "Speramus Meliora; Resurget Cineribus" which is Latin for "We Hope For Better Things; It Shall Rise From the Ashes". A motto that comes after Detroit burned to the ground in 1805, shortly after coming into US control. A motto that I believe still applies today.
Now, to dive into the heart of your question, what led Detroit from being on top of Industry and the world to being the butt of all our jokes. It's partly to blame on what brought Detroit so much success, the automotive industry. During the first half of the 20th century, Henry Ford perfected the assembly line. This allowed for anybody to own a car at a reasonable price, causing demand for cars to skyrocket. The auto makers in Detroit were doing everything they could to keep up with demand, expanding rapidly and hiring anybody they could.
Before Henry Ford's $5 work day, the turnover rate for factory employees was high. Ford wanted to retain his employees, and under the idea that each of his employees should be able to afford what they are producing, he introduced a $5 a day work day. Unheard of at the time, the $5 work day was introduced in 1914 and increased employee retention, and allowed for a factory job to become a factory career. This caused the citizens of Detroit to scramble for these new higher paying factory jobs, and ever since, the automotive industry has been the decisive driving economic factor in Detroit.
Beginning in the 1950s, the rapid expansion of the automotive industry began to slow down and even reverse due to increases in competition. It wasn't until the 2000s, however, that things came to a head. In 2008, General Motors and Chrysler went bankrupt, and Ford nearly did as well. Each of the companies were forced to make massive cuts, laying off thousands of employees. This caused a surge in the unemployment rate of Detroit and her suburbs. Since the key industry in the Metro Detroit area was the automotive industry, it forced thousands of families to go elsewhere to find work. This had a ripple effect through the economy of the area. With less people able to afford to spend unnecessary money and moving away, businesses unrelated to the auto industry took a hit. As more places closed, the economy got worse. Essentially a vicious circle of economic despair.
There is a disturbing racial element to this whole story as well. Beginning in the late 1950s and continuing into the 1960s, white families with good jobs in the auto factories started to move out to the suburbs of Detroit because more and more African-American families could afford to live in the nicer homes of Detroit, which has been almost exclusively white until this point (there are exceptions to this, and if you would like more information on earlier racial tensions in Detroit, I recommend you read up on the trial of Ossian Sweet). During the White Flight, real estate agents practiced discriminatory housing sales, separating hosing based on race. In 1967, racial tensions came to a head with the Detroit Riots. The three day riots saw the calling in of the Michigan National Guard, and 43 deaths. The most important aspect of the aftermath was the clear racial divide that was caused in Detroit. The remaining white families within the city borders fled to the outlying suburbs, while the African-American families were able to take over the nicer homes and essentially take control of Detroit proper.
Most of the white people I've talked to who have lived through this period of Detroit's history will say this is where the downfall of Detroit began. After the riots, the race of majority in the city limits was African-American, leading to the election of Coleman Young, the city's first African-American mayor. He came to power in 1974, and stayed in office for 20 years, until 1994. He was essentially fiscally conservative, cutting departments and rasising taxes to keep the budget balanced. However, his election may have served to deepened racial tensions between the city and the suburbs, but Young acted in ways that he thought was best for the city.
One of the major fiscal problems Detroit faces is paying off her pensioners. Currently there are more retired civic workers than current ones, and this creates a massive pension problem. These people felt entitled to their pensions, and it would have been a nightmare to try and cut from that (although it has happened recently by Emergency Manager Kevin Orr). Infamous Detroit Mayor Kwame Kilpatrick had an idea on how to keep up with increasing pension payments, and it included a complex scheme with Wall Street. Basically, Detroit would borrow huge sums of money from Wall Street to pay the pensioners, then bought derivatives at a fixed rate of 6%. The Detroit Free Press has an infograph to help visualize the complexity of the deal. Everybody at the time, even the Free Press, thought this was a good idea. However, the financial crisis of 2008 changed all that, turning this deal that was supposed to save Detroit into one of the final nails in her fiscal coffin.
Those are a few of the key reasons why Detroit is the way it is today. Of course, this is an incredibly complicated issue that is highly politicized today. There is an excellent Detroit Free Press article I am going to link to in my sources that goes into deeper depth on the collapse of Detroit.
SOURCES: Articles http://www.freep.com/interactive/article/20130915/NEWS01/130801004/Detroit-Bankruptcy-history-1950-debt-pension-revenue Lecture Notes https://www.evernote.com/shard/s122/sh/ac0afe12-5e2d-41df-b62c-e87fa6056259/99a16bb7375c7f6509dca61ae2f3cc85 https://www.evernote.com/shard/s122/sh/eb6b35eb-c207-45f0-87f1-ddc998428881/6cf3cdfbb28b0f70def5b937dabb9a7c https://www.evernote.com/shard/s122/sh/f24582fb-27af-4930-b50c-b0d2bf7c86b7/eaa9ccb917372ca7923b28af9d884888
A huge part if it was the creation if the massive freeway system designed in and around Detroit. These freeways laid waste to historic neighborhoods chopping up communities, increasing lead pollution from gasoline and just making the neighborhoods less appealing in general. The freeways meant you didn't necessarily have to live in Detroit to work there and during the 1850s and 1960s white families began trickling out of the city.
Speaking about work in Detroit during this era is difficult as well. Plants were closing after the war, some to reopen out of Detroit and some like the infamous Packard plant never to start operations again. Today there are only two car plants in Detroit.
When the riots happened well... The city never really recovered. Detroit had race riots dating back to 1863, another famously brutal riot in 1943, but the riot of 1967 is usually pointed out to be the culprit. After 1967 white flight went from a trickle to a tsunami.
Detroit is massive- you can easily fit New York and Chicago within the borders at the same time. Going from two million people to just over 700,000 people in a few decades meant that city services were strained by not enough taxes and too much area to serve.
Without service and with so many abandoned homes that no one had money to knock down property values dropped and people who staid in Detroit saw their home values plummet as the city became more and more uncontrollable.
The lack of authority and the obvious decline invites crime and mismanagement. Plenty of crooks in nearly every era of local government meant more wasted money, time and back sliding.
hi! you may be interested in these other threads related to urban decline, "white flight" and deurbanization in the US