Voltage Comparator resulting in low when I would expect high output
The LM339, like many other comparators, has an open-collector output.  The output is just the collector of an NPN transistor, which can pull the output pin towards ground, but cannot pull the output pin high.  If the output should be high, the external circuit must pull the output up.

If you connect the LED between V+ and the output pin, the LED will light when the output is low, and not light when the output is high.