"Specifically, Brebeuf Jesuit has respectfully declined the Archdiocese's insistence and directive that we dismiss a highly capable and qualified teacher due to the teacher being a spouse within a civilly-recognised same-sex marriage."
The unidentified teacher was said by Paulson to be "a valued employee" who does not teach religion. He wrote that Brebeuf Jesuit became aware through social media "that one of its teachers entered into a civil marriage with a person of the same sex".
According to the Associated Press, a school operated by the archdiocese, Indianapolis Roncalli High School, has fired or suspended two guidance counsellors in the past year because they are in same-sex marriages.
Brebeuf Jesuit's leaders who signed the open letter are the Rev William Verbryke, the school president; W Patrick Bruen, chair of the school's Board of Trustees; and Daniel M Lechleiter, chair-elect of the trustees board. They promised in the letter that the school's mission would not change as a result of this conflict with the archdiocese.
"We understand that this news will likely spur a host of emotions, questions and even confusion in the days ahead. Please be assured, the Archdiocese's decision will not change the mission or operations of Brebeuf Jesuit."
On Friday, the school's name was not on the archdiocese's list of Catholic schools in its region.
The church says there are 68 Catholic schools - 57 elementary schools and 11 high schools - in the Archdiocese of Indianapolis, according to its website. Collectively, they enrolled some 23,200 students during the 2018-2019 school year.
Most of those schools are operated by a school division within the archdiocese, which is headed by Superintendent Gina Kuntz Fleming, who did not return phone calls about Brebeuf Jesuit. While Brebeuf Jesuit is a Catholic school within the archdiocese, it is independently operated. The school has nearly 800 students in grades nine through 12.
The school leaders' letter says that, while the archdiocese "may choose to no longer attend or participate in the school's Masses and formal functions, Brebeuf Jesuit is, and will always be, a Catholic Jesuit school." It also says church leaders assured them that "Jesuit priests may continue to serve at Brebeuf Jesuit and will retain their ability to celebrate the sacraments of the Catholic Church".