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.
There is no venom more poisonous than that of the asp or cobra, and there is no evil greater than that of self-love. The winged children of self-love are self-praise, self-satisfaction, gluttony, unchastity, self-esteem, jealousy and the crown of all these, pride. Pride can drag down not men alone, but even angels from heaven, and surround them with darkness instead of light.
Since self-love is the origin and mother of evil, when this is eradicated all the things which derive from it are eradicated as well. For when self-love is absent, not the slightest trace or form of evil can exist in any way at all.
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.