I expect their point was that you bought the kitchen knife for cutting up food, and may have redeployed it to fend off an intruder, whereas there aren't many other reasons for owning an asp other than for hitting people with. It seems like the same sort of argument against owning a gun 'for protection', ie you've bought it with the specific intention of shooting someone, which isn't on.
Imagine walking to the shop in your lunch break with a pocketfull of screwdrivers - a policeman stops you and asks you why you've got them; the answer he wants to hear is "I'm an electrician and I use them for work", and not "for protection", although if someone tried to mug you it may be some defence to say you used whatever you had to hand in the situation.