What does Matthew 23:20 mean?

When people swear an oath, they are making a binding agreement to do what they say they will do. It is binding in the sense that both parties are held to their agreement according to the worthiness of what they swear on. That's why some informal modern oaths, at least in the English language, have included "swearing on your mother's life" or "swearing on a stack of Bibles." These were thought to be the most solemn and valuable things to which a person could attach such an agreement.

Religious leaders of Jesus' era, such as the scribes and Pharisees, taught the people of Israel to swear oaths on sacred things, like the gold in the temple or the gift on the altar. But they taught them not to swear on the temple or the altar themselves, as if some oaths were more binding than others. Jesus taught the people not to swear oaths, at all. Instead, they should simply be known for their integrity: to do what they say they will do (Matthew 5:33–37).

The point Christ makes in this criticism is not that there really are different levels of oaths. Rather, it's that it's absurd to separate one sacred thing from another. To swear by the altar of God in the temple is to swear by whatever is on the altar. The altar makes the gift or sacrifice sacred, because the one the gift is being offered to is holy. The Pharisees' teaching fits the caricature of a "blind guide" (Matthew 23:16) leading people in bizarre directions (Matthew 23:15).