Being on the receiving end of a correction can be painful. The best way to avoid it is to be free of moral and intellectual faults.
But if one who would admonish his brother in fraternal charity must be sure his authority will be recognized and his love perceived, one who would be admonished -- which is to say, one who is not certain he has no faults -- must recognize authority and perceive love.
Recognizing authority is a snap, since every Christian has made himself a servant of all, so all have authority over him.
Perceiving love can be more difficult; admonishers often betray no sign of the love with which they act. However, the Christian who has made himself docile to the will of God will know, even if he cannot articulate, the Divine love illuminating everything that happens to him, and so will be open to the correction given him.
Just because admonishment is a form of correction doesn't mean all admonishment is correct. Still, I think we can say as a general guideline that all admonishment should be accepted with gratitude -- toward God, at least -- and honestly evaluated. We are, after all, called to perfection, not adequacy, and it may be that even a completely wrong-headed attempt at correction leads you to see some fault you've missed before (like, for starters, dismissing out-of-hand completely wrong-headed attempts at correction).