Matthew introduces the idea of “loosing” in Matthew 5:19, though the same Greek word is here usually translated “breaks”:
Therefore, whoever breaks one of the least of these commandments, and teaches others to do the same, will be called least in the kingdom of heaven; but whoever does them and teaches them will be called great in the kingdom of heaven. (Matthew 5:19)
Here the improper loosing of a commandment makes one least in the kingdom… but still in the kingdom. When we get to the more familiar passages (Matthew 16:19; 18:18-20), it seems as though binding/loosing continues to apply to commandments rather than people. Rabbis in surrounding centuries also connect this language with deciding what Torah forbids and permits. It has implications for people, but what is actually bound or loosed is not people but rules.
More support for this reading comes from details of the Greek. According to David Garland,
The object of the binding and loosing is neuter (“whatever,” not “whoever”). They are not to bind or loose persons. The community is to do whatever is necessary to see that a little one does not perish, but it can make pronouncements on what is or is not sin with confidence. The final judgment of the individual, however, is still left to God. (Garland, Reading Matthew, 192–93)
In Matthew, Jesus gives the disciples the profound responsibility to interpret the First Testament in light of his own teaching and ministry. Like Jesus, they may tighten some portions while they set aside others, but only if they do so like Jesus. The early church appears to have taken this responsibility seriously. The Jerusalem council did not base their decision on any particular prooftext, but rather on what “seemed good to the Holy Spirit and to us” (Acts 15:28, especially in light of 10:28). Their decision would be a good example of “loosing” something by which people had previously been bound.