Well, that sounds logical. Strangulation could also be under 'personal weapon' since manual strangulation (using hands) is quite often the main method in strangulations.
Asphysixiation includes putting a bag on someone's head, putting a piece of cloth in one's mouth and nose, etc. but not strangling. It's the effect of strangling someone, but not a method of it. Though strangling should be part of 'personal weapon', the FBI decided otherwise.
The definition of asphyxiation is "the state or process of being deprived of oxygen, which can result in unconsciousness or death; suffocation." Isn't that usually the purpose of strangulation? To deprive someone of oxygen to the point of unconsciousness or death?