You have stumbled on the reason why people knowledgeable about the technical side and the business side are incredibly valuable. The following line from Tom Smykowski in the movie Office Space is actually relevant to every company:
Well-well look. I already told you: I
deal with the god damn customers so
the engineers don't have to. I have
people skills; I am good at dealing
with people. Can't you understand
that? What the hell is wrong with you
people?
You need someone with the right skills to do the following:
- Listen to customers' feature requests
- Determine what is desirable from a business standpoint
- Figure out of it's even technically possible
- Convey the customers' requests to the developers in a way a programmer can make sense of
I know it sounds really simple, but it's actually one of the most difficult challenges in business. There are a lot of smart MBAs and a lot of smart programmers, but finding a person with the right mix of those two is hard. My immediate thought when reading your question was "the people managing you don't have the right skill set". The person directly above you should have a strong technical background in whatever tools you are using. They should also have a good sense for business. The person above them really doesn't need to have much technical knowledge (if any), but they should be great at all things business. You should really be isolated from unrealistic customer demands. A good manager will do that. A good manager isolates you from worrying about the exact problem you mentioned in your question.
To try to answer your question: Try to think of real life scenarios that everyone experiences on a daily basis that just can't be done easily by computers. I found a book that might be perfect for you. It is called Computers Ltd.: What They Really Can't Do, and it describes seemingly "easy" problems that computers can't solve well. You might even suggest they read it. Hell! Buy them a copy as a gift! It will be well worth it for you.
Here is a quote from the Amazon description of the book:
This book puts the myth to rest that
computers can do everything. There are
certain types of problems that
computers just cannot solve and
probably never will be able to, not
unless you have a couple of zillion
years to wait for an answer! It is not
just complex problems that fall into
this category. Even seemingly simple
problems can beat the best computers
known to man. For example, assume a
traveling salesman has 100 towns to
visit. What town should he start at,
and in what order should he visit them
so as to reduce the number of miles he
travels to an absolute minimum? This
is a very difficult problem for a
computer to solve. This book tells you
why in a way that both the layman can
understand as well as being a good
introduction for budding computer
scientists everywhere.
In addition to the examples in that book, you can think of lots of everyday tasks that computers can't do well. Here are a few I can think of.
You give a computer a picture of a room full of various objects: chairs, tables, blocks, and a tricycle. Computers have an enormously tough time distinguishing individual objects in a field of objects. Even the best algorithms for doing so are unreliable and don't solve the real problem of distinguishing objects. They just recognize edges in pictures (oversimplified, I know).
Driving to work is really boring, so you want your computer to do it for you. Car companies have tried writing software to simply keep a safe distance from the car in front of you and failed miserably. Writing a program to merge onto a highway at 60MPH is many times harder than that.
Try writing a program to determine if a given thing is pretty or pleasing to look at.
Show them a CAPTCHA. Tell them a computer cannot recognize the word on the screen, even though they can do so without any effort at all.
Tell them that a legitimate, breakthrough, press-stopping milestone for Artificial Intelligence research would be creating a computer with the intelligence and critical reasoning capabilities of a three year old child.
Simply put, anything that requires a computer to decide anything without explicit instructions and criteria is difficult to impossible. Without previous input of some kind from humans, the best you can hope for is a random "decision". The input might be explicit, or it might be based on a pattern. It might even be something like the bayesian filtering in Thunderbird, which is ultimately based on flagging messages as spam or not spam.
It might be easier to start with things computer can do. They really can't do much, after you think about it for a while. They can add, subtract, multiply, and divide. They can read and write information from/to memory (variables). They can add and subtract different sets of numbers based on a comparison of two other numbers (conditionals). That's about it, really. There is a reason it's called programming: computers only do what we tell them to, nothing more, nothing less. There is no intuition, no free will, no curiosity, no imagination, no feelings, no common sense. Explaining it to them in such stark terms might help drive the point.