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.
As water standing behind an earth dam, and finding an aperture, washes it wider and wider and filters through it, if we do not strengthen the dam, or strengthen it insufficiently, at last, with growing weakness on our part and with repeated efforts, the water gets through with greater and greater force, so that at last it becomes very difficult, and even impossible to stop it; so also with malice hidden in the heart of man: if we let it pierce through once, twice, and thrice, it will pour out more and more powerfully, & may at last break through and overflow your dam.
There is a difference, Dearly Beloved Brethren, between the delights of the body and those of the soul, that the delights of the body, when we do not possess them, awaken in us a great desire for them; but when we possess them and enjoy them to the full they straightway awaken in us a feeling of aversion. But spiritual delights work in the opposite way. While we do not possess them we regard them with dislike and aversion; but once we partake of them we begin to desire them, and the more do we hunger for them. In one case the appetite pleases, the reality brings displeasure; in the other it is the appetite [that] displeases, the reality delights us more and more. In the one case appetite leads to fullness, and fullness to disgust; in the other appetite begets fullness, and fullness in turn begets appetite. For spiritual delights, when they fill the soul, increase in us a desire of them; and the more we savor them, the more do we come to know what we should eagerly love.
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.