Why is "door" pronounced with an "o" sound and not a "u"?

Because door is one of those words that have two O's because people thought that would make the O sound longer. Meaning longer in duration. In Old English the word was spelled dor with a long O. There was no character to write that kind of long O, so they figured the double O would make people hold the duration longer. Maybe it worked for a time, but obviously it failed somewhere over the past 1,000 years.