How do you mean all quadrilaterals are trapezoids?

We don't know who said that, but it's not true. Some quadrilaterals are trapezoids

and some aren't.

A quadrilateral is any drawing with four sides.

A trapezoid is any drawing with four sides and two of the sides are parallel.

So all trapezoids are quadrilaterals. But there are a lot of other quadrilaterals

that aren't trapezoids.