monoclinic is simply an extruded parallelogram. If we place end centers on parallelogram faces then taking half of both diagonals and same height as before as 3 basis, its the same. That's what I think. Can anyone clarify?
Here is my attempt at drawing the end centred monoclinic structure. The angles $a$ and $b$ are $90º$ and the angle $c$ is not. I've drawn two unit cells because the primitive cell spans two cells.
The primitive cell is in green. Hopefully it should be obvious that the primitive cell is not monoclinic because both the angles $b'$ and $c'$ are not $90º$. That's why we use the compound cell, because it increases the symmetry of the lattice.