what does this phrase mean 我偏不信邪
偏: (6) [adv] wilfully; deliberately; persistently
不信 = don't believe
邪: (2) disaster; misfortune (caused by evil spirits)

我偏不信邪
I, despite everything, do not believe there are supernatural coincidences
I insist, I do not believe there are supernatural coincidences

For example: You lost seven coin tosses in a row by choosing head, and for the eighth time, you still insist on choosing head, because having tail win eight times in a row is not scientific, the only way it could happen is there's some evil spirits power at work. And you don't believe there are evil spirits.
Well, if I lost seven coin tosses in a row, the most logical explanation I can think of is -- the other guy is cheating.