Did Paul disobey Peter?

Didn't St. Paul say something like this, "We resist you to the face" to St. Peter? That wasn't certainly being very obedient

I think perhaps you are confusing disobedience with fraternal correction. Paul did not disobey Peter, yet he did correct Peter when he believed him to have acted hypocritically.

Consider also St. Catherine of Siena, who taught with regard to obedience to the pope:

Even if that vicar were a devil incarnate, I must not defy him. (St. Catherine, Letter to Bernabo Visconti)

Of all the doctors of the Catholic Church, St. Catherine was one of the most ardent defenders of obedience to the Holy Father. Yet, she was also very critical of Pope Gregory XI in her letters to him. St. Catherine gently accuses the pope of neglecting his office through the sin of pride and self-love...

To you, most reverend and beloved father in Christ Jesus, your unworthy, poor, miserable daughter Catherine, servant and slave of the servants of Jesus Christ, writes in His precious Blood; with desire to see you a fruitful tree...

...Oh, sweet and true knowledge, which dost carry with thee the knife of hate, and dost stretch out the hand of holy desire, to draw forth and kill with this hate the worm of self-love--a worm that spoils and gnaws the root of our tree so that it cannot bear any fruit of life, but dries up, and its verdure lasts not! For if a man loves himself, perverse pride, head and source of every ill, lives in him, whatever his rank may be, prelate or subject.

... For he sees his subjects commit faults and sins, and pretends not to see them and fails to correct them; or if he does correct them, he does it with such coldness and lukewarmness that he does not accomplish anything, but plasters vice over; and he is always afraid of giving displeasure or of getting into a quarrel. All this is because he loves himself. Sometimes men like this want to get along with purely peaceful means. I say that this is the very worst cruelty which can be shown. If a wound when necessary is not cauterized or cut out with steel, but simply covered with ointment, not only does it fail to heal, but it infects everything, and many a time death follows from it.

Oh me, oh me, sweetest Babbo; mine! This is the reason that all the subjects are corrupted by impurity and iniquity. Oh me, weeping I say it! How dangerous is that worm we spoke of! For not only does it give death to the shepherd, but all the rest fall into sickness and death through it.

...Oh, human wretchedness! Blind is the sick man who does not know his own need, and blind the shepherd-physician, who has regard to nothing but pleasing, and his own advantage--since, not to forfeit it, he refrains from using the knife of justice or the fire of ardent charity!

...The cause of all this is, that he loves himself apart from God: so he does not follow sweet Jesus, the true Shepherd, who has given His life for His sheep. Truly, then, this perverse love is perilous for one's self and for others, and truly to be shunned, since it works too much harm to every generation of people. I hope by the goodness of God, venerable father mine, that you will quench this in yourself...I will, then, that you be so true and good a shepherd that if you had a hundred thousand lives you would be ready to give them all for the honour of God and the salvation of His creatures. ...

... there is a remedy for this, father: that we flee the love spoken of above, for ourselves and every creature apart from God. Let no more note be given to friends or parents or one's temporal needs, but only to virtue and the exaltation of things spiritual. For temporal things are failing you from no other cause than from your neglect of the spiritual.[St. Catherine of Siena, Letter to Pope Gregory XI, ca. AD 1375].

Catholics have the right, even at times the obligation to manifest their opinion in matters related to the good of the Church. This is affirmed in Vatican II's Dogmatic Constitution on the Church, Lumen Gentium. However, also within Lumen Gentium, is the obligation to be obedient to the decisions of the pastors of the Church.

By reason of the knowledge, competence, or pre-eminence which they have, the laity are empowered--indeed sometimes obliged--to manifest their opinion on those things which pertain to the good of the Church. If the occasion should arise, this should be done through the institutions established by the Church for that purpose, and always with truth, courage, and prudence, and with reverence and charity toward those who, by reason of their office, represent the person of Christ. The laity should, as all Christians, promptly accept in Christian obedience decisions of their spiritual shepherds, since they are representatives of Christ as well as teachers and rulers in the Church. [Lumen Gentium, 37]

See also: Charity Demands Fraternal Correction

God bless,

Dave