Matthew 6:3 - Ellicott's Commentary On The Whole Bible

Let not thy left hand know. — The phrase was probably proverbial, and indicates, in the form of free hyperbole, extremest secrecy. It is possible that there may be some reference to the practice of using the right hand in offering gifts at the altar. The symbolical application, though an afterthought, is yet suggestive. The “right hand” is the higher spiritual element in us that leads to acts of true charity, the “left” is the baser, self-seeking nature. We ought, as it were, to set a barrier between the two, as far as possible, i.e., to exclude that mingling of motives, which is at least the beginning of evil.