No one has any reasonable expectation of being at risk of being shot/stabbed.
The only reason, therefore, that you would wish to have access to something like bullet-proof clothing or ballistic protection is that you foresee it likely you will soon be in a situation whereby you will be shot at.
About the only conceivable situation that you are likely to be shot at is if you forsee yourself or are planning to be engaged in some type of violent action against a police/military force.
Therefore, the only people wanting bulletproof clothing are those planning violent action against a police/military force. And since no one else who is deemed "socially sane" has any desire to own such a peice of equipment, banning it comes with the two benefits of not curtailing normal citizen's freedoms, while adding an illegal thing/signal to the kind of people who do or would plan to do bad things.
Edit: I realise there is the additional possibility that the person seeking body-armour sees themselves involved in gun-fights with other gun-toting individuals/criminals. Even amongst the criminal classes (and certainly amongst civilians), that is seen as almost an equally preposterous/rare idea as gearing up to take it to the police...