The definition of a Bravais lattice is quite strict: Every lattice point experiences the same environment as any other lattice point, and the point symmetry of the lattice must be respected. Some combinations of erystal systems and centering types do not exist. For example, in the tetragonal system, the only Bravais lattices are $tP$ and $t.$ To understand the concept of a lattice and why other tetragonal lattices do not exist, start with a primitive tetragonal unit cell.

Centre the $B$ faces. Show that the resulting lattice is not a new one because there is an existing Bravais lattice $($with a lower symmetry$)$ that is reproduced by this centring operation. $($No cell transformation is required.$)$

Centre the A and $B$ faces. Show that the result is not even a lattice in the sense that the definition of a lattice point is violated! $($Here$,$ it is useful to draw the local environments around these points.$)$

Centre all faces. Show that the resulting lattice is not a new one because there is an existing tetragonal Bravais lattice that is equivalent. $($Here$,$ a cell transformation is useful to show.$)$