Show willingness by tidying the wires in your bedroom as an example of how it's possible to make a safe environment for a cat. (Be careful handling plugs and cables; if necessary, unplug electrical equipment from the mains or turn the power to the socket off). Show your parents what a good job you did, and offer to cat-proof the rest of the house. If they are unconvinced, ask them if this is the only reason they don't want to get a cat and to be honest about why.