That's not exactly true. Corporations have many of the same rights. For example, in Citizens United vs FEC, the Supreme Court wrote that:
"The Court has recognized that First Amendment protection extends to corporations (...) The Court has thus rejected the argument that political speech of corporations or other associations should be treated differently under the First Amendment simply because such associations are not 'natural persons'."
(page 25 in https://www.supremecourt.gov/opinions/09pdf/08-205.pdf )
If the First Amendment is the recognition of a right, then corporations have that right, just like natural persons. This concept in the US is called "corporate personhood" and it has long been recognized by courts:
https://en.wikipedia.org/wiki/Corporate_personhood#Case_law_...
> In 1818, the United States Supreme Court decided Trustees of Dartmouth College v. Woodward (...) Beginning with this opinion, the U.S. Supreme Court has continuously recognized corporations as having the same rights as natural persons to contract and to enforce contracts.