If the scientific study of language is by its very own nature descriptive not prescriptive, why is linguistics a science?

Well, as Zeibura S. Kathau has commented, Science is by nature descriptive. And linguistics is a science. A very soft science, I’ll grant you, but no less of one than geology or astronomy.

There’s a word for fields of study that say how things should be, rather than how things are. That word is not science. It’s engineering.

No value judgement hither or thither, btw. There is a role for language prescription in the world. Linguists dislike it because it gets in the way of their job; but then again, linguists are often prejudiced against looking at the social context of their object of study.