I don't need any polarizer. I have a normal portrait using the mirror without using polarizer.
Ok, I don't dispute that YOU don't need this.
My dispute is with your statement "There is no different with shooting directly." I think I explained this adequately in my response to you. The rest of my response, below, is mainly for other readers who may not follow that gist.
What I'm saying is simply, if one uses a (smallish) on-camera flash as the sole illumination to take a self-portrait in a mirror, then a very substantial glare will exist in the image. (The small area of the flash is producing 100% of the illumination of the subject, and consequently must appear much, much brighter than other parts of the scene.) However, the use of two polarizing filters, as I initially described, can DRASTICALLY reduce the photographed glare from the flash head, making it nearly insignificant in the photograph. As a wild guess, I would say perhaps 98% or more reduction.