I also went through a phase where quantum entanglement seemed mundane and easily explained. However, I realized that this was merely because I was taking the analogies too literally.

The key difference between a bag of coins and a microscopic quantum system is that the contents of the bag before being observed is unknown, whereas the quantum state is actually indeterminate. By observing one entangled particle, you force the other to also take on a definite state. Read up on Bell's inequality for the experimental justification of this idea.