What if I say that the mirror doesn't flip left and right? You've heard it right the mirror doesn't do the flipping. As the above answers say the mirror shows what is right infringe of it. It's you(we humans) who think it is flipping.

**Let me get this in detail**

Before we begin tell me ,'What makes you think that the mirror flips your left and right?'
Or may be 'what image do you it flips?'
The second question is a follow up question of the first one.

To answer these questions you need a camera not just an ordinary camera an imaginary,invisible camera
{ i.e i(camera) i,as in x+iy not in iPhone *pun intended*}

Now take a picture of yourself (No, not a selfie)with that camera at a distance x and at height of your eye from ground. What do you sees?
you will see a picture of 'beautiful you' in that picture with your left and right **unswapped**

Now place the mirror facing you at a distance x/2 from you while you are standing still ( now you know why I said,no selfie) 

Now take a picture of the mirror with the cam at your eye (I know it's practically not possible but trust me  this 'i' can do anything) what do you see? You will see the same 'you' as beautiful as you were in the first pic but with your left and right **swapped**

Now you see that the image is a flipped left and right.