If I die….

Our school provides a life insurance policy at no cost to all teachers. The benefit (if you die) is one year’s salary OR $50,000, whichever is less. That is to help your family recover from your death, make funeral arrangements and supplement the family income. I get that. I think that’s a really good thing.
The school is also offering SUPPLEMENTAL life insurance so that death benefit (I know it sounds weird, but isn’t that really what it is?) can go up to as much as $100K. The cost is really minimal and if you sign on now, there is no physical, etc. I get that, too, and I think that’s also a really good benefit IF YOU NEED IT.
One of the teachers asked me if I was going to take advantage of it. My response was (and I didn’t mean to sound sarcastic or morbid; it was just my observation) “I don’t have a family to worry about leaving any money TO. Why do I need it?” It took him back a little, but I asked again (and my principal was there, too) “Correct me if I’m wrong, but life insurance is to help your family recover when you die? Isn’t that the purpose?”

Am I wrong?