I first heard a variant of this on my first day of work at my first permanent job. One of the senior management staff said, "No one is indispensable". To a newbie, fresh out of school, it felt extremely grating to the ears. And then you wake up one day while you're on leave, to scores of unread email, your blood pressure rising as you scroll through said emails and epiphany strikes... I am not indispensable. People will find ways to cope with my absence. If I reply to those emails, I'm encouraging them to continue sending me emails, and I'll have more to clear later on. So I replied to the 2 most urgent emails rather tersely and ignored the rest. They can wait. I need to concentrate on this exam prep or i'll have to re-take in another 6 months!
Just a place for me to write...