A Catholic high school in Indiana has fired a gay teacher to avoid losing its “Catholic identity” and being removed from the Indianapolis Catholic Diocese.

Cathedral High School explained the situation in an open letter Sunday, describing the decision as "agonizing."

The letter says that Archbishop Charles Thompson made clear that "continued employment of a teacher in a public, same-sex marriage would result in our forfeiting our Catholic identity."

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"If this were to happen, Cathedral would lose the ability to celebrate the Sacraments as we have in the past 100 years with our students and community," the letter, signed by Cathedral’s board Chairman Matt Cohoat and President Rob Bridges, reads. "Cathedral must follow the direct guidance given to us by Archbishop Thompson and separate from the teacher."

Last week, the Archbishop issued a decree prohibiting Brebeuf Jesuit Preparatory School, another area school, from calling itself Catholic or being identified as a Catholic institution after it refused to fire a gay teacher.

Brebeuf Jesuit Preparatory School said in a letter last week that obeying the Archbishop's instruction would cause “harm” to its teachers and staff, and that while it is “disheartened” by the decision, “our identity as a Catholic Jesuit institution remains unchanged.”

Officials at Cathedral High School acknowledged that there may be some backlash to their decision to fire the teacher, who was not named in the letter.

“In today’s climate, we know that being Catholic can be challenging and we hope that this action does not dishearten you, and, most especially, dishearten Cathedral’s young people,” they wrote. “We know that some individuals do not agree with every teaching of the Catholic Church and so their conscience struggles between the teaching and what they believe is right. We want you to know that we respect an individual’s conflict between teaching and their conscience.”

The Indianapolis Catholic Diocese did not immediately respond to a request for comment on Cathedral's decision.