The author believes we are “endangering our health by not using the metric system.” do you agree or disagree and why?

I agree with the author. By using the metric system we know the exact amount of a medicine we took, whether it's in mg or mL. This way every doctor can prescribe the same amount.
If we were using some other units this may not be the case. For example, british and american inch were different until 1950's.

Example: if you go to a surgery and a doctor needs to cut "1 inch from the left part" it may cause a mistake as this unit is different in different countries. But if he needs to cut "2.5 cm from the left part" he knows exactly where to cut.

Another benefit of using metric system is that it is being used in almost every country in the world.