Two wrongs do not make a right, and in our irritated or angry impatience, we frequently say or do something just as bad or worse as was done to us! Then where are we? Often, our patience does not delay our wrath as God's does.
The obvious meaning of Paul's advice is that we should not take vengeance. In Romans 12:19, Paul repeats this more plainly:
Beloved, do not avenge yourselves, but rather give place to wrath; for it is written, "Vengeance is Mine, I will repay," says the Lord.
This, in turn, feeds directly into Jesus' teaching in Matthew 5:39-45, where Jesus' consistent instruction is that we not set ourselves against an evil person who is injuring us, whether verbally, physically or judicially. Rather, Jesus teaches us to be willing to give the offender something that might defuse the immediate situation—and perhaps even provide some small example that will promote his eternal welfare. Patience is of great value in this respect.
This in no way means we are weak, though to them we may at first seem so. Nor does it mean that we approve of their conduct. Though we may hate their conduct and suffer keenly when it affects us, Christ tells us to bless them, meaning we should confer favor upon or give benefits to them. We can do this by wishing the person well, speaking kindly of and to him, and seeking to do him good.
Situations like this may be the most difficult test we will ever face. Patiently deferring retaliation and committing the circumstance to God's judgment are indispensable to the best possible solution. But the primary point of Jesus' instruction, however, is not how to resolve these situations, but that we may be children of our Father. By imitating God's pattern, we will resemble Him and take a giant stride toward being in His image.