Why do my eyes always turn out blue in pictures despite them being darker in reality?

Possibly reflections. When a photo is taken of your eyes the light reflected or bent back to the camera is a function of the light in the room, the way the camera is angled, and other factors that influence the recorded color of your eyes in the picture. What you see in the mirror is a direct reflection of your eye color as you see it, so that is more likely to be the perceived color.