Why do prices of all cryptocurrencies move in sync? For example, when bitcoin moves up/down, most other cryptocurrencies also move for a similar amount. What is the reason behind this? I almost see no point in investing in different cryptocurrencies, when it seems that when Bitcoin falls, Ethereum (or any other crypto) also falls.

Only reason I can figure out myself is because all cryptocurrencies belong into the same group of currencies, but is there something else that affects these same price changes?
The reason 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.