II. Hilary is disturbing the peace of the Church by his insubordination.
But with the approval, as we believe, of God, and retaining towards you the fullness of our love which the Apostolic See always, as you remember, expends upon you, holy brethren we are striving to correct these things by mature counsel, and to share with you the task of setting your churches in order, not by innovations but by restoration of the old; that we may persevere in the accustomed state which our fathers handed down to us, and please our God through the ministry of a good work by removing the scandals of disturbances.
And so we would have you recollect, brethren, as we do, that the Apostolic See, such is the reverence in which it is held, has times out of number been referred to and consulted by the priests of your province as well as others, and in the various matters of appeal, as the old usage demanded, it has reversed or confirmed decisions: and in this way “the unity of the spirit in the bond of peace” has been kept, and by the interchange of letters, our honourable proceedings have promoted a lasting affection: for “seeking not our own but the things of Christ,” we have been careful not to do despite to the dignity which God has given both to the churches and their priests.
But this path which with our fathers has been always so well kept to and wisely maintained, Hilary has quitted, and is likely to disturb the position and agreement of the priests by his novel arrogance: desiring to subject you to his power in such a way as not to suffer himself to be subject to the blessed Apostle Peter, claiming for himself the ordinations of all the churches throughout the provinces of Gaul, and transferring to himself the dignity which is due to metropolitan priests; he diminishes even the reverence that is paid to the blessed Peter himself with his proud words: for not only was the power of loosing and binding given to Peter before the others, but also to Peter more especially was entrusted the care of feeding the sheep. Yet any one who holds that the headship must be denied to Peter, cannot really diminish his dignity: but is puffed up with the breath of his pride, and plunges himself into the lowest depth.
Source: Letters (New Advent)