Why do altcoins vary so along with bitcoins?
The answer is that many altcoins are traded in BTC/ALTcoin pairs, not $$/ALT pairs. 

So if an altcoin is trading 0.1 BTC/ALT, and the dollar price of bitcoin falls, then the $ price of the ALT will fall an equal amount. 

Some altcoins trade against dollars as well, so their dollar price may be less coupled to the BTC dollar price. But for many of those alts, a large amount of the trading volume will still be from the BTC/ALT pair, and so the influence is still there.