Fr. Corapi clarifies that he is not leaving the Church.

Vocation was to preach.
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Fr. Corapi's latest statement is interesting, wherein he explains that he is not leaving the Church nor the priesthood - he is simply not going to be ministering publicly as a priest, and only in that sense he will be working outside the Church.  I'll let him tell it.
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June 23, 2011
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I think it’s a bit too easy to arrive at an erroneous conclusion when you base it on a fallacious presupposition. For instance, some very kind and fine people assume that I have “left the Church.” Please, understand this, I have not left the Church. I love the Catholic Church and would not “leave the Church.” I have resigned from public ministry, which is rather anticlimactic to be sure since I was out of it anyhow due to the suspension or “administrative leave,” which is tantamount to suspension. There are elements of this that you don’t know about, and that’s not your fault.
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Once a man is ordained a priest he remains a priest for all eternity. Holy Orders is one of the three sacraments that imprints an indelible mark on the soul. What the Church can give or remove is “faculties”, which authorizes the person to publicly administer the sacraments.
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The leadership of the Church has made it clear to me they don’t want me anymore. They have a right to do that and I have to accept that. So, I’ll do what I can outside of the Church. I’m not leaving the Church. I am simply doing something else in life so that I won’t wither up and die, and so that you can still derive some benefit from my gifts from God. It may not be as good as before, or it may be better. The only thing I know for sure is that I’m not going to disobey the Church and attempt to “minister” as a priest, and I’m not going to lay down and die. I’m not ready to do that just yet. As a matter of fact, you might be pleasantly surprised at what’s in our future. Stay in touch. We may not have the old meeting places anymore, but we have some new ones and I would like to meet you there. - Blacksheepdog
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Doing as the bishops say, but not exactly how they expected you to do it.
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I'm very much reminded of Mother Nadine Brown who has also determined to continue her ministry while remaining Catholic.
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When Brown made her move, she too had consulted lawyers, canonical as well as civil. It seems to me, agree with her or not, she acted within her rights as a baptized Catholic lay person.  Mother Nadine and companions were never excommunicated or placed under interdict, although their Public Association was canonically suppressed and they were dispensed from their religious vows.  (I've been told these were private vows and they were not technically religious.)  As a lay person, Nadine Brown appears to be acting within her rights and is not using the name "Catholic" except to identify the Companions as a group of Catholic laity.  Brown's statement doesn't mean she is not a faithful Catholic either - she did exactly what the Archbishop asked her to do.

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Sadly, neither of these situations inspire confidence in the bishops of the Catholic Church for the followers of these ministries.