"Under God"

Is the phrase "under God" in the Pledge of Allegiance unconstitutional when recited in a teacher-led pledge, even if recitation of the pledge is not mandatory? I think so. Teacher-led school prayer, even at a football game, is considered to be unconstitutional. So shouldn't direct acknowledgement of God be considered unconstitutional as well? The original version of the Pledge of Allegiance did not even have the phrase "under God" in it. This was added in the 1950's to taunt the Soviet Union, which was atheist. So, why do we still have the phrase, even after the Cold War has been over? It serves almost no purpose other than to taunt those who do not believe in a higher power. David Souter stated that "Government shall not prefer one religion to another, or religion to irreligion." Isn't saying that we are a nation which is under God as an enactor of the state a blatant preference of religion to irreligion? Why should the government say that we are under God when we are an expressly secular country? Can you imagine the public outcry if there were a "one nation against God" phrase in the Pledge of Allegiance? How is that not equivalent to saying that we are a nation which is under God?