The next quality of love is also stated many different ways: "not irritable", "not provoked", "not easily angered", etc.
This sounds very similar to patience. (Short fuse/long fuse.) I think that the effect is the same in the two qualities (a lack of getting back, revenge or retribution), but they come from different perspectives.
Imagine an acquaintance getting into your face, screaming at you and accusing you of something that is totally false. The normal, initial reaction would be to sense the falsehood, feel the injustice, and yell back. Maybe even getting physical somehow.
Patience would feel the offense, but hold onto the reaction. It would not explode, even though it would want to. Does it see the explosion as not being positive? Does it see the explosion as not helping the other person? Both?
Not being provoked would take a mental step backwards. It would recognize the falsehood. It might also recognize the pain it is feeling. But it might also recognize the pain behind the person screaming. If it did, it would try to cross the boundary between the two people, and try to understand what was going on. It might say things like "if someone said/did something like that to me, I would be angry too" or ask "how do you know I said/did this?"
Two different attitudes and responses to adverse circumstances. Both fly in the face of the natural, expected reaction. It is this counter-cultural response that stands out. It is this sort of non-natural, non-normal reaction that demonstrates the power of Jesus' love, and Jesus' love in us.