It matters because that means the AR-15 has a rate of fire comparable to a handgun, as opposed to the much higher rate of fire the assault rifles available to the military are capable of. So by calling semi-automatic rifles assault rifles, it is making the rifle seem more dangerous than it actually is in an effort to convince people to ban them.
If your claims about yourself are only remotely true, you must have shot something like a 9mm semi-automatic pistol and an assault rifle in your life. And still you claim they have comparable rate of fire in semi-automatic mode? Sure, theoretically, if you put both of them in a strong vise and measure how fast you can pull the trigger you might end up with a comparable rate. In practice not only is aiming much faster with an assault rifle (given the same distance to target), but also your shot doesn't throw the gun off target nearly as much as a pistol shot does and you don't have to readjust your position as much. If you had a three-round burst setting on a 9mm pistol, your third shot would certainly be going up into the sky, far away from any target.
The rate of aimed fire is much higher with a semi-automatic assault-style rifle than with a military-grade semi-automatic pistol. Add the extended range, the much better precision and the higher bullet velocity and you have a weapon that is far deadlier than any semi-automatic pistol.