[roughly]

"People" in this case is a legal term, not a colloquial one. Nobody's arguing that corporations are not composed of people.

And, arguably, yes, the same argument applies to the legal personhood of a forest - that proving that the impact on a group of trees aggregates to something significant and legally actionable is unnecessarily time consuming to keep doing every time someone tries to argue their clear-cutting operation hasn't actually harmed anyone, so you assign legal personhood to the forest so you can say "you harmed the forest" in the same way you can say "you harmed the corporation."