In Supergirl Season 1 finale, Non and Indigo have triggered a device that is going to kill all of humanity in the next 4 hours. Martian, the only other superhero around, is hurt. No normal human is able to get close to the device to assist Supergirl and Supergirl has to go on a suicide mission to try to fight Kryptonians. If she loses or if they just stall her long enough, all humans of earth die.
What is the compelling reason for her to not call Superman? The situation is dire enough.