A design pattern I've noticed on internet banking sites is that you get automatically logged out and sent to a warning page if/when you hit the back button on your browser, ending your session and obliging you to log in again.

I'm presuming this is due to some sort of security consideration, but I'm at a loss to figure out what. What is the rationale for this behaviour?

A scenario such banks might want to protect you from could be this:


you visit your banking website and do your banking stuff.
after you are finished you log out and then navigate to some other website to look at cat pictures or whatever.
you leave your computer with the cat picture website open. Because there is nothing incriminating on your screen, you feel safe doing that.
your evil roommate comes along and presses the back button a few times.
they arrive at the cached version of your banking site, see your bank account and see that you still haven't paid your share of the rent even though you clearly have enough money to do that.


That's one reason why banking websites do not work when you navigate to them using the browsers back button.

But an even more likely reason could be laziness on the side of the web developers. 

Allowing the user to use back and forward navigation creates an additional variable in a web application which needs to be kept in mind at all times.  Simply making this impossible removes that variable and makes it far easier for the developers to create a secure and bug-free application. Because bugs in banking applications can cause quite a lot of financial damage, developers in that sector are rather conservative and tend to limit usability when it results in a more predictable application use-pattern.
