Jump Around by House of Pain (never was a band so aptly named). It's the repeated high-pitched "Wiiieeeeeeeeeeeee, wiiieeeeeeeee", I find literally painful.
To a lesser extent, Crazy Horses by The Osmonds for the same reason but at least it's mitigated by it's early environmentalist message.
I assume the OP means she turns off anything released pre 1960. I'm kind of with her there but in my case it's anything pre-1970 with the honourable exceptions of The Kinks, The Stones and a few other individual tracks. I like to wind fans of 60s music (esp Beatles) up by saying "Bless, they were just learning how to make decent music, like stabilisers on a bike".