It isn't that it is too complicated to explain, just that's it's too complicated to have just happened by random chance. Big difference.
No scientist claims evolution happens by random chance. The spin of a roulette wheel produces random results, but the house always wins. This is easy enough to observe and document. There is no magic involved. The house does not have to cheat.
Play roulette long enough and the house will have all of everyone's money. Randomness does not preclude movement toward order.
Not to be lawyerly about this (he said, leaving himself wide open), I suppose that depends on your definition of "random." If by random, you mean "without cause," then I would agree entirely with you. Once you proceed beyond principal causation, however, the issue gets murky. Even by fairly basic Biblical precepts, God is not a necessary driver for the minutia of His creation to operate.
Congratulations. You have just concurred with, albeit unintentionally, the theory of evolution.