Failing using startx to launch different desktops

Question

I am trying to use startx to launch different desktops according to an argument using case...esac

This is my .xinitrc

mate(){
    (sleep 5 && conky) &
    mate-session
} 

case $1 in
    d2) i3;;
     *) mate;;
esac

When I use startx launches by default mate (as it should be). However, when using startx d2 nothing happens.

What I am doing wrong?

EDIT:

I've just found out that using xinit d2 it launches the desktop environment but not with startx d2