37 In the next place, He goes on to say: “And if your right eye offend you, pluck it out, and cast it from you: for it is profitable for you that one of your members should perish, and not that your whole body should go into hell.” Here, certainly, there is need of great courage in order to cut off one's members. For whatever it is that is meant by the “eye,” undoubtedly it is such a thing as is ardently loved. For those who wish to express their affection strongly are wont to speak thus: I love him as my own eyes, or even more than my own eyes. Then, when the word “right” is added, it is meant perhaps to intensify the strength of the affection. For although these bodily eyes of ours are turned in a common direction for the purpose of seeing, and if both are turned they have equal power, yet men are more afraid of losing the right one. So that the sense in this case is: Whatever it is which you so love that you reckon it as a right eye, if it offends you, i.e. if it proves a hindrance to you on the way to true happiness, pluck it out and cast it from you. For it is profitable for you, that one of these which you so love that they cleave to you as if they were members, should perish, rather than that your whole body should be cast into hell.
38. But since He follows it up with a similar statement respecting the right hand, “If your right hand offend you, cut it off, and cast it from you: for it is profitable for you that one of your members should perish, and not that your whole body should go into hell,” He compels us to inquire more carefully what He has spoken of as an eye. And as regards this inquiry, nothing occurs to me as a more suitable explanation than a greatly beloved friend: for this, certainly, is something which we may rightly call a member which we ardently love; and this friend a counsellor, for it is an eye, as it were, pointing out the road; and that in divine things, for it is the right eye: so that the left is indeed a beloved counsellor, but in earthly matters, pertaining to the necessities of the body; concerning which as a cause of stumbling it was superfluous to speak, inasmuch as not even the right was to be spared. Now, a counsellor in divine things is a cause of stumbling, if he endeavours to lead one into any dangerous heresy under the guise of religion and doctrine. Hence also let the right hand be taken in the sense of a beloved helper and assistant in divine works: for in like manner as contemplation is rightly understood as having its seat in the eye, so action in the right hand; so that the left hand may be understood in reference to works which are necessary for this life, and for the body.
Source: Our Lord's Sermon on the Mount (New Advent)