Does it have to be on a Monday?

No!  You might just want to reduce your meat intake overall, or choose a different day of the week.  After all, some people like to eat their left overs from Sunday dinner on a Monday!  However, it can be helpful to stick to a particular day especially if you are doing it with others at school or at work, to help to keep the momentum going!   And perhaps if we all make that effort, one day really can make a world of difference!