Let's look at this rationally

At the beginning of every adult life lies a lifetime of potential earnings. This is the money that you will make, over your entire life, if the income from your chosen profession remains constant and rises steadily in a logical manner.

This is the income that you and your family depend on. If you die, that potential income disappears. You are no longer around, therefore you cannot, no matter how badly you may want to, earn that money. For your family, having become dependent on that income for a certain standard of life, this can be a financially devastating loss on top of the emotional devastation.

Ok, so you can't do anything about the emotional loss, no money will cover that, but you can do something about the financial loss by protecting against the potential loss of your potential income.

That's life insurance.

By buying a life insurance policy now, when you are young and healthy, you can make sure that your family, if you die prematurely, will receive an amount of money that offsets the risk of your premature death and loss of future earnings.

It's not pretty, but it makes sense.