Mate and Cinnamon differ by one basic thing; The first lays upon software rendering, the latter uses video card acceleration.
This is why, with Cinnamon you get so called "graphical effects", dynamically resizing widnows etc.
One of the reason of the information you're given is that your video card doesn't support 3d acceleration, thus Cinnamon switches to 2d rendering.
However. It is quite impossible to point to one, unique reason without knowing what your videocard is. So, start with telling us that
Unless you removed it Mate should still be present in your login manager dropdown-menu. It's enough to choose it and log in.