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.
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.
An old man was asked, 'How can I find God?' He said, 'In fasting, in watching, in labors, in devotion, and, above all, in discernment. I tell you, many have injured their bodies without discernment and have gone away from us having achieved nothing. Our mouths smell bad through fasting, we know the Scriptures by heart, we recite all the Psalms of David, but we have not that which God seeks: charity and humility.'