spiders, centipedes and pretty much most bugs bigger than an ant, had trouble killing them even with a paper towel. Hell used to get afraid looking at them in pictures.
To overcome it, I built a "weapon" to kill them with. Pretty much took one of those post office poster rolls, and attached some paper towels to it. This way I could kill them at a distance.
Now, have no problem getting upclose and personal and killing them with a paper towel. Can now watch them online without any problems(i.e. one of those giant centipedes eating a rabbit)
I dunno if it's something I overcame on my own, or if its something I just grew into. i.e. I used to be scared shitless of the Alien and the Predator movies, and now I more or less consider the series as an action movie, instead of a horror flick.