What does Matthew 5:20 mean?
Jesus has been forceful and clear about a point that can be difficult to understand: He has not come to abolish the law of Moses, but to fulfill it. It will not pass away until all has been accomplished. Those hearing Jesus' message should not be lenient on themselves or their students about obeying the commands of the law. Those who obey them will be called great in the kingdom of heaven; those who do not carefully obey will be called the least. This doesn't suggest that good deeds earn salvation, but it does make an important point about God's intent for those prior messages (Matthew 5:17–19).Now Jesus demands a standard which would have sounded impossible to His listeners—exactly how it is meant to be taken. Scribes were professional experts on the Scriptures. The Pharisees were a sect famous for their extremely careful keeping of the law of Moses. They were so careful, in fact, that they added layers of detail, rules, and regulations on top of the law so they'd never come close to breaking it. Pharisees were extraordinarily strict with their students and with the common synagogue-goers about what it took to follow the law in order to be righteous.
Jesus is making two distinct points here. Matthew has already shown that the righteousness of the scribes and Pharisees is false. John the Baptist called them out as a "brood of vipers" in need of a repentance that will actually "bear fruit" instead of just looking good to other people (Matthew 3:7–8). Jesus, too, will clash with the Pharisees over the way they work so hard on outward appearances while sin decays their hearts. As Jesus will emphasize in the rest of this sermon, God cares far more about what is in a person's heart than how other people perceive them. God values true purity motivated by true love more than technical rule-keeping motivated by spiritual pride. So true "righteousness" is something better than the rotten version paraded by religious hypocrites.
The other point being made, which upcoming teaching will support, is that nobody can be truly, perfectly righteous. No person can live a life of moral purity worthy of heaven. As Paul will write in Romans 3:23, "for all have sinned and fall short of the glory of God." He will add, though, in the following verse what Jesus' listeners will come to understand later on, that those who come to faith in Christ "and are justified by his grace as a gift, through the redemption that is in Christ Jesus" (Romans 3:24). Jesus is prepping His listeners to understand that they need a righteousness only He can earn for us.
