Some people are afraid that unscrupulous people will use the serial ## in illegal or immoral ways. Most commonly they fear that someone will report the gun stolen, using the serial # to make it sound credible. This may get the actual owner in trouble. It sounds like something someone with a grudge might do....maybe someone who wants the gun and doesn't understand how the law works.
I don't know if it's ever actually been done, it may be one of those "urban myths" that float around -- especially on the 'net.
Others may do it just out of privacy concerns.
And some others out of fear the government will be able to make a list of guns the people own.
I have no real idea how valid these peoples' concerns are over this. I have posted photos of some of my guns and without concern for the serial #. The only reason I see to actually post it is on old guns, they can help you track down the date an old gun was made. Say you inherit your grandpa's 1873 Winchester. There are books about Winchesters that list date of manufacture by serial # and if you don't want to buy the book you post the gun here with atleast all but the last two digits and someone will likely be able to help you.