You ask for some way of completely eradicating irritability. The inclination to irritability is given us to use against sin, and we were never meant to use it against our fellow men. When we do, we act contrary to our true nature.
When the blessed Eulogius saw an angel distributing gifts to the monks who toiled at all-night vigils, to one he gave a gold piece with the image of Our Lord Jesus Christ, to another a silver piece with a cross, to another a copper piece, to another a bronze piece, and to another nothing. The others who had remained in the church, left the church empty-handed. It was revealed to him that the ones who had obtained the gifts are those who toil at vigils and are diligent in prayers, supplications, psalms, chants, and readings. Those who received nothing or who left the church empty-handed are those who are heedless of their salvation, are enslaved to vainglory and the clamors of life, and stand feebly and lazily at vigils and whisper and jest.
We ought not to grieve or become irritated at anything because, by frequent vexation and irritability, we form the morally and physically very injurious habit of irritability, whilst by bearing opposition with equanimity we form the good and useful habit of enduring everything calmly and patiently.