Question

why does face centered tetragonal crystal do not exist while face centered cubic crystal does exist ?

Answer 1

A face-centered tetragonal cell can be drawn. Two are shown in orange, below.



But this diagram also shows that the face-centered tetragonal cell is part of a lattice where a smaller body-centered tetragonal cell can be chosen (edges outlines in blue). It is simply conventional to choose the simpler, smaller body-centered tetragonal cell.