Compare it to a plane, Nimsooze and you may get the idea. Imagine an airplane sppeding down the runway. People expect that it will take off and fly but it never gets off the ground, it never is successful.
"it unfurled its triumphal course only to unravel its own progress at every point"
Here, it seems this "project" is being compared to a flag. Iimagine a flag that is rolled up. It is then unfurled, exposed to the weather/wind. As that happens, the material of the flag unravels/falls apart either partially or completely; another unsuccessful try.
"do sth only to do sth else" - people often believe they have a good plan and try something without sufficient planning or without thinking of the implications. When they launch their plan, it doesn't go as expected for any number of reasons.
The sentence seems to be saying that "modernity" never adequately planned for success.
Student or Learner