What happens to my Bitcoins if I leave them at Coinbase after the hard fork? So I have a few hundred dollars worth of bitcoins that I bought at Coinbase. I basically just bought them to figure out how to buy bitcoins. 

Anyway, it was going to cost like $2-3 in transaction fees to move them to an external wallet so I basically decided to just keep them at Coinbase for now, even if it is the unsafe thing to do, seeing as it's only a few hundred dollars.

I just received an email from Coinbase saying that after the fork, they will only support the current version of bitcoins (BTC) and that I would not be able to withdraw the BitCoin Cash (BCC) ones.

My understanding is that after a hard fork, basically everyone gets their bitcoins duplicated. One BTC and one BCC. So given that Coinbase isn't supporting BCC, what happens to my BCC bitcoins? Are they lost somehow?

Also, I thought that my Coinbase wallet would be exactly the same as any wallet you can get on a computer / wallet. Why is it then that if I keep my coins up on Coinbase, I only get the BTC but if I have it on my own computer, I would get to have both the BTC and BCC bitcoins.
This is what Coinbase says about the November 2017 expected hard fork:
Customers with bitcoin balances stored on Coinbase at the time of the fork will have access to bitcoin on both blockchains. There is no action required from customers and bitcoin can be securely stored on Coinbase before, during, and after the fork. Read more about it here: 
https://blog.coinbase.com/update-on-the-bitcoin-segwit2x-hard-fork-69426f14bc85