Well, there is a perfectly logical reason for your body to act this way, and it may have saved one of your ancestors lives back in the day.
“There is a plausible evolutionary reason for syncope (SING-kə-pee), or fainting, at the sight of blood: the drop in blood pressure is a response adapted to minimize the loss of one’s own blood. With lowered blood pressure, the volume of blood that’s lost from an open wound is significantly diminished, perhaps sometimes being the difference between life and death.”
“Though sometimes the sight of someone else’s blood still activates this adapted response in people. Apparently, evolution has an itchy trigger finger.”