Over the last few years I've worked in a number of companies as a software developer, with industries ranging from manufacturing to banking and finance. 

Unfortunately, it seems that I haven't really made the most of these opportunities to learn about the industries involved. For example, I worked in a major investment bank for over a year, but I can't really say I know much more about finance and banking than the average joe.

I believe it is in part due to the nature of my work which generally has been writing software for database access, charting, and data manipulation. There is no business benefit for anyone to tell me any more, so it's up to me to learn and find out more on my own.

How would I go about trying to find out about the company and what it does, and how the industry works?

I've tried talking to people at lunch breaks and inviting them for coffee, etc. with mixed results. Primarily I've found that many people are reluctant to take me up as part of their "network". I suspect it is in large part because they don't see how they would benefit as in their eyes I'm "just an IT guy" which to some people has the same status as kitchen staff.

Am I doing something wrong, or is the prospect of "start with XXX job and work your way up" just a myth?