Why is it we can't just get along? Why is it when we have problems, we are not able to work together in a civil manner to solve those problems? Why is our first inclination to say, “It's the other guy's fault” rather than simply looking for a solution for our common good?

God gets to the heart of the matter:

What causes fights and quarrels among you? Don't they come from your desires that battle within you? You want something but don't get it. You kill and covet, but you cannot have what you want. You quarrel and fight. You do not have, because you do not ask God. When you ask, you do not receive, because you ask with wrong motives that you may spend what you get on your pleasures.
James 4:1-3

Jesus taught:

The good man brings good things out of the good stored up in his heart, and the evil man brings evil things out of the evil stored up in his heart. For out of the overflow of his heart his mouth speaks.
Luke 6:45

What we let our minds dwell on, not only comes out our mouth, but also in our actions (James 1:13-15). Everyone has a “sinful nature” which we either resist or allow its free rein (Galatians 5:19-21.) We are given instruction on what inclinations are sinful and the power God makes available to resist them.

So I say, live by the Spirit, and you will not gratify the desires of the sinful nature. For the sinful nature desires what is contrary to the Spirit, and the Spirit what is contrary to the sinful nature. They are in conflict with each other, so that you do not do what you want. But if you are led by the Spirit, you are not under law.
Galatians 5:16-18

Some interpret “not under law” as meaning you do whatever you think is right without considering God's instructions, his law. No one is “justified” or made righteous by the law (Galatians 2:17-21; 5:4), but God by his Spirit enables us to want to live righteous lives. It is a matter of “heart”—a strong inner desire to yield to God's goal of creating us in his image. If we serve gods of lust and greed, selfishly putting our own unlawful desires ahead of the interests and needs of other people, we cannot put on the likeness of Christ.

The law, including the Ten Commandments, teaches us what not to do. Yet, we are also commanded to “love your neighbor as yourself (Leviticus 19:18.)” Who among us has ever completely obeyed this command? Paul exhorted the church in Galatia:

You, my brothers, were called to be free. But do not use your freedom to indulge the sinful nature; rather, serve one another in love. The entire law is summed up in a single command: “Love your neighbor as yourself.” If you keep on biting and devouring each other, watch out or you will be destroyed by each other.
Galatians 5:13-15

The solution to all the fighting and quarreling is pretty simple, but very difficult to do without the Holy Spirit's power motivating and enabling us. To avoid destroying one another, love God completely from the heart and love and treat your neighbor in the same way you desire to be loved and treated.