I had the same logic as you previously, actually. But, eventually, I realized the terminology is not as misleading as it appears.
Try defining what is "people". What is "natural people". Why do "natural people" have "rights". What is a "corporation". How does a "corporation" differ from any other legal fiction. So on.
Try defining what is "people". What is "natural people". Why do "natural people" have "rights". What is a "corporation". How does a "corporation" differ from any other legal fiction. So on.