Why does a corporation have the same rights as a person?

Because the author of the 14th Amendment said so.

“Which gets us to the chief action to which Bingham was called, when he worked to secure the interests of RR companies – namely, liberating corporations from state control by inserting the word ‘person’ into Fourteenth Amendment language, thereby qualifying naturally avaricious, potentially immortal wealth accumulation machines for the same protections freed slaves were soon to enjoy.”

“The Crafting of the Fourteenth Amendment”

http://www.frontporchrepublic.com/2014/03/crafting-fourteenth-amendment/