The argument that Obama and the ATF are using is not only that this ammo is armor piercing but, more importantly, that there are now handguns that are capable of firing these bullets. If there were never handguns capable of firing the 5.56/.223 ammo, the President would never have been able to issue a ban. Under a 1986 law -- Law Enforcement Officers Protection Act of 1986 -- it was legal to sell armor-piercing ammo as long as it was only used in rifles.
The reason for this exemption was logical because rifles, of any kind, are little used in murders in this country; let alone the murder of cops. For example, in 2013, the FBI reported that of the 8,454 firearm murders that year, only 285 were caused by rifles with most of those incidents occurring in home invasions or neighborhood or family disputes. Not in the killing of cops. The simple fact is that rifles aren't used in the commission of most crimes because they aren't concealable; either before or after the crime. But, when you have a firearm that looks like this (below) and is capable of piercing a light-weight police vest, you have a major problem under that 1986 law:
The above gun is one of the potentially concealable Kel-Tec PLR16 5.56/.223 handguns (pistols) which probably prompted the ban on the .223/5.56 ammunition. Others like it are either available now or will be soon.
So, simply, Obama wants to show that he is doing something about mass shootings by killing off weapons that look too militaristic such as the AR-15; even though an AR-15 is rarely used in any murders let alone mass shootings because, again, it can't be readily concealed. But, the fact that he can now do this, was handed to him on a silver platter by the firearm industry itself. Thus, with a stroke of a pen and the slim possibility of any valid legal challenge in the courts, Obama will starve much of the AR-15's out of existence for lack of ammunition.
The only way this action might be reversible is if the firearm industry decides to voluntarily stop making 5.56/.223 handguns. But, this might not be doable because the cat is already out of the bag.
ATF proposes banning 5.56mm/.223 caliber ammunition used in popular AR-15 style rifle: http://fox43.com/2015/02/26/atf-proposes-banning-5-56mm-223-caliber-ammunition-used-in-popular-ar-15-style-rifle/
Law Enforcement Officers Protection Act of 1986: http://www.gpo.gov/fdsys/granule/STATUTE-100/STATUTE-100-Pg920/content-detail.html
Expanded Homicide Data Table 8: http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2013/crime-in-the-u.s.-2013/offenses-known-to-law-enforcement/expanded-homicide/expanded_homicide_data_table_8_murder_victims_by_weapon_2009-2013.xls
WTS Kel-Tec PLR16 .223/5.56 Pistol: https://www.ar15.com/archive/topic.html?b=7&f=88&t=458952