I have asked that question to the internet community awhile ago and there wasn't any answer out there. All the information the search provide provided is "how to remove emblem". Before one learn how to remove it, one question comes to everyone's mind is 'why should I?'. I have done my research and decided to share what I learn here.
One main reasons to remove the emblem is to keep your car stealth. Just like the car plate, the emblem is a piece of identification. It goes without saying that everyone will remove their car plate if it is not require by law. However remove emblem is not illegal. One less emblem, one less piece of identification. Stealth.
Other reasons to remove the emblem is to improve MPG by:reduce unnecessary weight, improve body contour, remove air trap pocket. Remove the emblem give your car a smoother look and feel, and easier to wash.
Also, the auto makers are getting free advertisements by putting their logo on the car you brought from them. And if you got an expensive car, removing the emblem will protect it from protect it from potential theft.
You might want to keep the emblem if you want to sale it later. also if you brought the car purely to show-off what car you have, you might want to keep the emblem.
If your car is old and you don't plan to sell it, there is no reason to not remove the emblem.