You are thinking "I am going to clip this red rectangle with a black circle" but that is where your problem is.
The clipping object has no color, so you'd have to think of this as three objects. An invisible clipping circle, a black something-bigger-than-the-circle, and your red rectangle. Once you realize that it will solve the problem.
So make a big black square, a red rectangle, and then put a green circle on top. Do a multiple select where you start with the circle, then select the other two. Then make the clipping mask.
Let me also point out that pathfinder won't help you with this kind of problem. It only makes one path - so one fill folor. The moment you want to make two colors of fill you have a problem that needs multiple paths.
If that's okay, you could use pathfinder. Just make a copy of the circle, and then intersect the copy with the red object. Then have the intersected red object on top of your circle. You could make a group so they'd move together, but you couldn't resize the circle and have it show more or less of the red, because you've cut the red up. Obviously not as good as a clipping mask but sometimes you have to do it.
Another thing you can try is live paint. What that does is it basically takes all the shapes and the points they intersect define the lines and areas you can paint. So if you draw a black circle and red rectangle, then select them both you can say "Object-Make Live Paint Group". Then you could tell it to make the bottom half of the intersection of the rectangle with the circle white, and still move the rectangle. Another option.