Because when you make group of $2$ then you will get $\mathbf{n-1}$ elements.
$\mathbf{Eg}$:
Let's say given elements are: $\{1,2,3,4,5\}$
Now you want to group $\{1,2\}$
So, total elements would now be:
$\{\enclose{circle}{\underset{{\text{count as 1}}}{1,2}},3,4,5\}$
So, total elements are :$5-1 = 4 = \mathbf{n-1}$