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.
The closet of the soul is the body; our doors are the five bodily senses. The soul enters its closet when the mind does not wander hither and thither, roaming among things and affairs of the world, but stays within, in our heart. Our senses become closed and remain closed when we do not let them be attached to external sensory things, and in this way our mind remains free from every worldly attachment, and by secret mental prayer unites with God its Father. 'And thy Father which seeth in secret shall reward thee openly,' adds the Lord. God who knows all secret things sees mental prayer and rewards it openly with great gifts. For that prayer is true and perfect which fills the soul with Divine grace and spiritual gifts.
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.