Hardwood and softwood trees

I read some unusual articles from time to time, but this paragraph in The Conservation article 'The secret stories of trees are written in the knots and swirls of your floorboards. An Expert explains how to read them' is a little more perplexing than most.

Hardwoods are, by definition, flowering trees, while softwoods are from cone-bearing trees. Paradoxically, not all softwoods are soft or hardwoods hard. The balsa tree, for example, is a fast-growing hardwood tree renowned for its soft wood.

I thought the purpose of classifying things was to assist you understand them, but I guess there are always exceptions.