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A state function can be defined by a start and end point. Work is quantified based on the pathways you take. For example, if two people exert a force over a certain distance to the same destination, but take different paths with varying distances, the path matters. So you can't quantify work with only two points.
Work is not a state function be use it is path dependent so it matters which route you take. Since displacement is needed, it is not a state function. The work you put into getting up to your dorm room by walking around the building, then to Bcafe, and up the stairs is different from the work of just walking directly to your room. By definition, a state function is a property that depends only on the current state of the system not how it got there.
Another way to look at this is graphically. If you take the graph of P and V, and you plot two points (final and initial), you can draw any amount of curves to connect these points. However, since work is the area under the curve of this graph, some curves will have a bigger area and some with a smaller area under the graph, so work DOES depend on the path taken and therefore its not a state function.
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