Of course they would feel threatened. For many years they were the sold and solid institute where people seek financial assistance and security. Bitcoin cannot be manipulated by them thus could destroy their industry.
Threatened should not be the proper word here. Bitcoin is not threatening anyone, not even the banking system. Bitcoin and banks should work together. However, what banks is afraid of is that with Bitcoin, we are totally eliminating them. No middle person like banks. We are our own banks. However, both of them can work mutually exclusive. At least we have other options and I'm don't think most of the bitcoin users are anti-banks, there are still bitcoin users who store their wealth in a banks. And we can't totally eliminate banks. They have to think it that way. There's no way that they will became obsolete because of bitcoins. Banks are here to say and so is bitcoin. No one will win in this war. And they should not be nervous nor feel threatened in anyway by bitcoin.