Depending on how often you shampoo, the first wash can serve to moisturise the scalp and hair follicles. Consequently, your first wash and rinse can often leave ...well...I suppose the best word for it is residue..think of it the way you would with your washing machine. It uses the first wash to remove all the primary bits and bobs, and the second cycle is a bit of a rinse out.
No, you won't lose your hair. Our society tends to be a bit obsessive about these things due to pressure from media and societal judgements.
If you also use conditioners each time, you 'may' find there's an excessive build-up and in that instance, having a couple of good washes, and forgetting about the conditioner for the day could give your hair a bit more bounce and shine.
If you don't like the idea of the second wash, but appreciate the idea of cleaning out any other bits...try mixing 2 parts white vinegar to 4 parts water...it will do the same thing and is great for helping your brush move through your hair afterwards.
Best of luck
Fr Bill