Correction is not an easy thing to give or take. I am terrible at taking correction. I get defensive, I try to justifying myself, and I get offended. That's not a good thing. No matter who we are we must always be open to correction. We are not a perfect people so we are going to be wrong sometimes and need to be open to a person of maturity coming alongside to help us see where we are wrong. Sometimes correction comes directly from the Spirit but other times God will use an earthly vessel.
Just as hard is to be that earthly vessel God wants to use to bring correction. I always consider that to be holy ground. I never rush into correction remembering how I feel about being corrected. I surround the moment in prayer and approach it with humility but I must be obedient in it. There is a lot at stake for the other person as God wants to bring them back in alignment with his heart. There must also be the attitude that I am not responsible for their reaction. If they receive the correction, that's great. If they become angry and refuse the correction, they can deal with the Spirit in the matter; I have been faithful to my part.
When Paul had to confront Peter with his hypocrisy in Antioch it must not have been an easy thing to do. This is Peter we are talking about, one of the great pillars of the Church. Everyone knew of Peter and he would have been approaching the status of legend at this time but what he was doing was wrong and Paul was given to deal with the matter. Many years after the fact Paul wrote to the Galatians:
When Peter came to Antioch, I opposed him to his face, because he was clearly in the wrong. (Galatians 2:11)
It was worse than just Peter being wrong, he was also leading others into the same hypocrisy. Unfortunately that is the danger of "pillars" going wrong, they bring others along with them:
Before certain men came from James, he used to eat with the Gentiles. But when they arrived, he began to draw back and separate himself from the Gentiles because he was afraid of those who belonged to the circumcision group. The other Jews joined him in his hypocrisy, so that by their hypocrisy even Barnabas was led astray. (Galatians 2:12-13)
So according to the Law a Jew could not associate with a gentile unless he had converted to Judaism and even then his contact was to be limited. It was certain they could not eat with them. They were so strict about this that, if you recall, Peter had to explain his actions to the other Apostles in Jerusalem when it was discovered he had entered Cornelius' home, even though it was in obedience to Jesus. So here was Peter, the great pillar, eating with the Gentiles unless people from James, the leader of the council in Jerusalem, the brother of Jesus, were paying a visit. Consider how Paul handled it.
"When Peter came to Antioch ..." Paul waited until the right moment. Sometimes correction is done in a rush so it is done incorrectly. Rushed correction, or reactionary correction often causes worse problems than the thing being corrected in the first place. Correction should never be done in anger, in fact there should be as little emotion involved in it as possible except that which is provoked by compassion. Correction should always be seen in love and never in revenge or hatred. If you feel your emotions provoked in a negative way then it is not the right time to bring in correction.
"... I opposed him ..." Fully understand the perspective you are coming from. You are opposing this person you are correcting. It is important to understand this so you are not shocked by any negative reaction. As I said at the beginning, it is not always easy being opposed. Some of us have a bad reaction to it because of our lack of maturity in it. If a person is mature they understand that correction is a healthy thing, it is for their benefit but we don't always see it that way. so it is best to be prepared.
"... I opposed him to his face ..." This is very important. If you have to correct someone make sure that you do it face to face. As long as it is in your power to do so, do not write them a correction, do not do it over the phone, give them the dignity of seeing your face. So in other words, don't be a coward about it. And don't do it by talking behind the person's back. Don't start a whisper campaign by telling others that the person is wrong. Deal with it face to face. To be corrected is bad enough but for others to hear of the correction before you do is far worse. That speaks to the lack of maturity in the corrector and it is best that correction not come through such a person.
Do not take any pride in being chosen to bring correction. It is a very humbling position because it reminds you of all the times you have needed correction. It reminds you of how immature you have been in the correction you have received. It may even highlight many of the things you need correction for in your life now. Correction never comes from the perspective of superiority or perfection; it comes through humbleness. No, correction is not an easy thing to take or to give and yet it is good for us and our relationship with Jesus. Taking a slogon from an old cough medicine commercial, "It tastes aweful and it works".