Because to find change in velocity you have to subtract the initial velocity u from the final velocity v.
To do this you reverse the initial velocity (makes it -u) and then add to v making it v + (-u) = v-u
On the vector diagram you do this by starting the second vector at the tail end of the first vector and not the head. If you were to combine the vectors at the head of the first you would be adding and not subtracting.