Well, I can't really define Metal, but I can show you how to tell them that Nu-Metal (I prefer to call it NO-Metal) isn't Metal at all.
1) Metal has a meaning, not just "fuck fuck fuck".
2) Metal musicians RESPECT their fans, they don't go on stage like "SHUT THE FUCK UP YOU MOTHER-FUCKERS!", etc...
3) Metal musicians are SKILLED musicians, not people who grabbed their instruments and decided to see how much noise they could make with them.
4) Metal has Melody/Harmony.
5) Metal doesn't have ANYTHING to do with shitty rap, or hip-hop (unlike Nu-Metal).
6) Metal is a cult, Nu-Metal is a trend.
7) Metal isn't noise, it's agressive. Nu-Metal isn't agressive, it's noise.
8) Metalheads HEADBANG, they don't jump around kicking each other.
9) Metalheads have respect for each other! The community stays together!
10) Metalheads know what a double bass is. This is hard to believe, but I showed "Silent Night, Bodom Night (Live In Japan)" from Children Of Bodom to a nu-metal freak around here to show him what true music was, and his comments were: "Man, that music sucks, but the drummer is a damn machine gun! he doesn't stop!" And while saying that, he was moving his arms around like when hitting a snare drum, thinking that's how they did the double bass.
11) Metal musicians know how to make SOLOS!