All the diagrams showing how massive bodies warp the space/time continuum (causing what we consider gravity) show the continuum as a 2-dimensional graph. Why is it planar and not 3-dimensional?

The problem is that, from the perspective of our senses, we live in a three-dimensional world and are unable to visualize a four-dimensional universe. Space time, therefore, has four dimensions: three spatial dimensions and time.

Therefore, we reduce the number of spatial dimensions to two in order to visualize curved space time and provide an analogy.

In other words, the vertical axis in the diagrams represents time, and the horizontal surface represents two dimensions of space. To put it another way, the more space that is stretched into the time dimension, the slower time passes.

The diagrams simplifying gravity often depict a 2D plane to illustrate the warping of space/time in a clear and understandable manner. In reality, the warping occurs in three dimensions. The 2D representation is a visual aid to convey the concept more easily.