Glennon was later named Coadjutor Archbishop of St. Louis on April 27, 1903. He succeeded Archbishop Kain as the fourth Archbishop of St. Louis upon the latter's death on October 13 of that year. Realizing the Cathedral of St. Louis could no longer accommodate its growing congregation, Glennon quickly began raising funds for a new cathedral, the cornerstone of which was later laid on October 18, 1908. He opened the new Kenrick Seminary in 1915, followed by the minor seminary in Shrewsbury. He delivered the eulogy at the funeral of Cardinal James Gibbons, and was appointed an Assistant at the Pontifical Throne on June 28, 1921. He opposed British rule in Ireland, and supported the leaders of the Easter Rebellion. The Archbishop once lamented the fact that women were competing with men in the workforce, saying, "Some of the women go downtown in the race and race beside the men...It is regrettable that men have to let them, are compelled to let them." Following the bombing of Pearl Harbor in 1941, Glennon declared, "We are not a military nation, but we are at war.... Churches have a duty in time of war not to promote hatred, racial or otherwise. Churches should give their moral aid and their physical support to the nation." He was an outspoken opponent of divorce, saying, "The modern attitude makes a joke of the sacrament of matrimony." He also condemned gambling games as "unworthy of our Catholic people...causing much scandal," and prohibited dancing and drinking at church-sponsored events. The Archbishop sometimes threw the opening ball for the St. Louis Cardinals, but did not play any sports himself, once saying, "I once tried golf, but I so disfigured the scenery that I never played again, in fear of public indignation and reprisal." Despite a rather popular tenure, as Archbishop of St. Louis he opposed racial integration in the city's Catholic schools, colleges, and universities. During the early 1940s, many local priests, especially Jesuits, challenged the segregationist policies at the city's Catholic schools. The St. Louis chapter of the Midwest Clergy Conference on Negro Welfare, formed locally in 1938, pushed the all-female Webster College to integrate first. However, in 1943, Glennon blocked the enrollment of a young black woman at the college by speaking privately with the Kentucky-based superior of the Sisters of Loretto, which staffed the college. When approached directly by pro-integration priests, Glennon called the integration plan a "Jesuit ploy," and quickly transferred one of the complaining priests away from his mission at an African-American parish. The Pittsburgh Courier, an African-American newspaper with national circulation, discovered Glennon's intervention and ran a front-page feature on the Webster incident. In response, Father Claude Heithaus, professor of Classical Archaeology at the Catholic Saint Louis University, delivered an angry sermon accusing his own institution of immoral behavior in its segregation policies. Saint Louis University began admitting African American students that summer when its president, Father Patrick Holloran, managed to secure approval from the reluctant Archbishop Glennon. Nevertheless, St. Louis maintained one of the largest numbers of African-American parishes and schools in the country.