We live in a society in which admitting one’s own sins is seen as a sign of weakness.
The Church of England has consecrated Libby Lane in a ceremony at York Minster.
The Reverend Libby Lane, 48, has been ordained as the new Bishop of Stockport in front of more than 1,000 people.
The Church formally adopted legislation last November to allow women bishops, following decades of argument over women's ordination.
Archbishop of York John Sentamu, who led the service, said he had been "praying and working for this day".
During the two-hour service Dr Sentamu and other bishops laid their hands on Mrs Lane and prayed. This was followed by lengthy applause.
A man interrupts the ordination of Libby Lane as bishop, calling it an "absolute impediment"
Writing in today's Yorkshire Post the archbishop said: "It is high time we had women bishops. I have been praying and working for this day.
"In a few years' time when more and more women will be bishops, I predict we shall be wondering how we ever managed without them."
However, in an indication that some Anglicans still oppose women's ordination, the service was briefly delayed by an opponent of the changes.
The Rev Paul Williamson stepped forward shouting "not in the Bible" after the Archbishop of York asked the church if Mrs Lane should be ordained as a bishop.
The second time Dr Sentamu asked the congregation, there was no opposition and the ceremony continued.
A Church of England spokesman said of Mr Williamson, priest in charge of a church in Hanworth, Middlesex: "He's got the right to protest but the contrast was between a lone voice protesting and a sea of voices affirming."
Mrs Lane had said the consecration would be a very "emotional" moment.
She said: "It is a remarkable thing that this happens to me, and people have been very supportive of me personally, but actually this is about a moment in the Church's history."
Speaking after the service her son Benedict said: "We've been building up to it now for a long time and it's satisfying that it has finally happened and we are finally here.
"She's the best person for the job."
Mrs Lane has been vicar of St Peter's Hale and St Elizabeth's Ashley, in Greater Manchester, since April 2007.