She's right it's an immune response, warts are caused by a virus. You can cut it off and keep freezing the base, you can also go buy some trichloroacetic acid TCA 50% on the web, take a needle, dip it, touch it on there,and it will frost (it's not freezing, it just turns white), let that part die, then in a week do it again. This acid will eat a hole right through you so don't use more than one teensy tiny bit at a time, but you should be able to get rid of it, be very careful. They sell TCA for women's wrinkles, they water it down and paint it on and their face sheds and voila, fresh skin, but if you use it direct it will take that thing away pronto. Get adult supervision though.