I think you mean the three project constraints, and not objectives. There is a huge difference between a constraint and an objective. (Note: I have tagged your question accordingly)
The main reason of the tradeoffs is that any one of these constraints can affect the others.
For example, let's say that you are working on an IT project that is over schedule, throwing more money at it (and as such affecting the cost constraint) will probably solve the problem. Reducing the quality may also solve the problem.
Think about the three constraints as the angles of a triangle. The total degrees in an angle is always 180 degrees - if one angle changes, then at least one of the other two will change.