The First Amendment to the United States Constitution brings the Free Exercise Clause, in which grants all citizens the right of freedom of religion. Therefore, one can interpret that it is allowed for anyone to organize prayers due to this freedom of religion.
However, the First Amendment also brings the Establishment Clause, in which says the Congress should not make laws respecting an establishment of religion nor prohibit the free exercise of it.
Both clauses conflict because on the one hand, citizens are allowed to manifest their religion, and on the other hand the government can not manifest support to any religion.
Therefore, organizing prayer session in a public school can harm the Establishment Clause that prohibits the state of supporting religions, since a public schools are financed by the government.
