I don’t think banks are the ones against Bitcoin. It should be the government that is against Bitcoin because they don’t have control over it. The banks actually report to the government and because Bitcoin isn’t doing the same, they don’t like it. Because starting from tax and other things they’d have implemented or rule they’d have set, they can’t. Bitcoin takes out the middle man and the government can’t do nothing about it, no matter much they dislike it.
The question is s, who's the bank and who's the government? They are same set of people under the financial system and their interest, policies and objective are twined. The banks are more like an agents of the government through which the government can use to bar and frustrate any other rising financial system that tend to be of a treat to their power of control and bitcoin is one of such with it's decentralized protocol. Which makes puts me in the right by referring the bank as a middle too.
Nonetheless the bank and the government are not the same. Understand the difference that the bank is not owned by the government. There are many private owner and they don’t have any personality in the government. However, the government under policies use the bank to do and get whatever they want. And that’s because banks follow policies which are set by the government. So government may use the bank as a tool but they are not one.