The archbishop also lamented that Martin "suggests that Catholic teaching on same-sex attraction as 'objectively disordered' (for example, in CCC 2358) is cruel and should be modified."
That suggestion "misrepresents Catholic belief," Chaput said.
"It's worth recalling here that the Catechism also describes lust, extra-marital relations, and contracepted sex (2351), masturbation (2352), and even non-sexual sins such as lying and calumny (1753), as intrinsically 'disordered.' The suggestion that the wisdom of the Church, rooted in the Word of God and centuries of human experience, is somehow cruel or misguided does grave harm to her mission. Families have been destroyed because of this misperception, and Father Martin regrettably contributes ambiguity to issues that demand a liberating biblical clarity," the archbishop added.
For his part, Martin tweeted a response to Chaput's column Thursday morning. The tweets took the form of a letter to Chaput.
"I think my main response is that it's difficult to respond to critiques that I am 'implying' things, when I am assiduous in my writings and talks about not challenging church teaching," Martin wrote.
Martin noted that the lecture he offered at St. Joseph's University "is the same lecture that I presented at the World Meeting of Families in Dublin last year, the text of which was vetted and approved beforehand by the Vatican."
Acknowleding that same-sex relations and same-sex marriage are impermissable and immoral, Martin tweeted that "LGBT Catholics have heard this repeatedly. Indeed, often that is the only thing that they hear from their church."
"What I am trying to do instead is encourage Catholics to see LGBT people as more than just sexual beings, to see them in their totality, much as Jesus saw people on the margins, people who were also seen as 'other' in his time," the priest wrote.
During his World Meeting of Families lecture, which Martin said was the same lecture he gave in Philadelphia this week, the priest criticized "homophobic pastors" and said that "LGBT people bring special gifts to the Church, like any group."
Chaput's column, which explained that he was unable to prevent Martin from appearing at a Catholic college overseen by a religious order, also criticized "bitter personal attacks" against the priest from other Catholics.
"As I've said previously, such attacks are inexcusable and unChristian."
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Nevertheless, the archbishop said, he had a responsibility to raise objections to some aspects of Martin's message.
"Supporters of Father Martin's efforts will note, correctly, that several Church leaders have endorsed his work," Chaput concluded.
"Those Churchmen are responsible for their words -- as I am for mine, as pastor of the Church in Philadelphia. And specifically in that role as pastor, I want to extend the CDF's caution to all the faithful of the Church in Philadelphia, regarding the ambiguity about same-sex related issues found throughout the statements and activities of Father James Martin."