Why is subtracting a negative number a positive number?

It is a double negative, subtracting is essentially adding a negative, therefore subtracting would be a negative negative number, which would be a positive, my mom helped me remember it by thinking if a bad thing happened to a bad person, it would be good, if a good thing happened to a good person it would be good, if a bad thing happened to a good person it would be bad, ect.