Draw a quadrilateral that have 4 sides, opposite sides equal ,and no sides are perpendicular?

Any parallelogram that's not a rectangle meets those qualifications.

Start with a rectangle made out of popsicle sticks or stiff wire.
Then sit on it.  Lightly.  Not enough to break it, just enough
to make it lean slightly out of shape to one side.

Whose mistake? can you give more details to what the question is asking?