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)