"Patience" is the first quality of love. We generally define patience as perseverance when confronted by a delay or adverse circumstances.
Patience in the Bible is usually seen in the context of personal interactions. And interacting with people does not always go smoothly. There are some people, when they encounter a problem, who has what is described as a "short fuse." A person runs into a problem, the fuse is ignited and an explosion soon follows.
A short fuse is the opposite of patience. Patience is a long fuse. Patience is tying more fuze, onto the original fuse once it is lit, so it takes longer to explode.
Eventually, anger becomes an appropriate response to cruelty, dishonesty, or injustice. Patience keeps anger in check, or in control. We all know of, or have experienced, instances where uncontrolled anger has caused damage, perhaps disproportionate damage.
Patience demonstrates God's nature, because God treats us with patience. We have all broken God's law. God is completely justified with condemning us ... now. God could judge us right now. But he has a long fuse, because he expects, and works toward, people choosing to establish an allegiance with him. He expects something good to happen.
What if we approach people, expecting something good to happen, when the only thing in evidence is something bad? What if we gave people room to change? What if we invited God to work, and then waited for it to happen?
Maybe that is the fundamental reason for patience. We can have a positive response to people, because we know God is in control ... and we can wait for him to act.