The majority of violent crime in the UK is not committed with firearms.
Police officers are mostly unarmed, as are security guards, and most people in general.
A violent criminal can achieve their goals using knives, matches and other type of weapons.
This means that criminals do not feel compelled to use a firearm in a robbery or a mugging.
(and it also means that less legal firearms are stolen and find their way into the hands of criminals)
If someone is attacked at home by an axe wielding burglar, I am sure they'd love to have a firearm to hand, and at the individual level this makes sense.
However, at the community level, if more police officers, security guards, and private citizens arm themselves with firearms for self defense, then inevitably criminals will up their game to match and we will see many more violent crimes where a firearms was used by the perpetrators.
Not sure that we want this.