Possibly because the first time that pupils are introduced to the name and concept it is has only two dimensions. These are usually represented as horizontal (x) and vertical (y) coordinates.
Actually, many children meet the concept - in its 1-dimensional form - as the number line. It is not called a Cartesian coordinate system then, and they make only simple use of it.
The Cartesian coordinate system is normally extended to 3-dimensional space in high school coordinate geometry when it is obviously not called a plane, and to multi-dimensional hyperspaces in advanced mathematics or physics.
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The coordinate plane is sometimes call the Cartesian plane because Rene Descartes is often credited with inventing the coordinate plane and so the coordinate plane is sometimes called the Cartesian plane,in his honor.
A coordinate plane is sometimes called Cartesian plane in honor of René Descartes. YOU ARE AN IDIOT
x-y plane
plane xy
It is simply called a point in the coordinate or Cartesian plane.