If the Spirit brings unity then it only follows that the flesh brings disunity because the two are antithetical to each other. In Greek the word flesh is sarx (you get that in the word sarcophagus = flesh + eater). In its most basic sense the word sarx means our physical flesh, the part of us that covers our bones (BDAG). But flesh can mean more than that. Here is the thing about the nature of flesh. Flesh is corruptible. It is decayable. That is what it does because of what sin and death have done to our bodies. The fleshly component of our physical bodies is also part of what gets redeemed and restored in the resurrection which is why Paul says in 1 Cor 15 that death is an enemy to be defeated and that in the resurrection we truly will have bodies but not bodies of sarx in all its decayable properties but bodies of a spiritual nature, which are still very much bodies. That's another point for another article but it is still one more piece of the puzzle that spirit and flesh stand in opposition to each other. I am not talking about Platonic dualism where material things are bad and spiritual things are good. I am talking about a particular characteristic of our earthly bodies, not material things in general.Paul contrasts life led by the Holy Spirit vs life led by the fleshly desires in Romans 8. Here is what he wrote,

Romans 8:1-4:"Therefore, there is now no condemnation for those who are in Christ Jesus, ² because through Christ Jesus the law of the Spirit who gives life has set you free from the law of sin and death. ³ For what the law was powerless to do because it was weakened by the flesh, God did by sending his own Son in the likeness of sinful flesh to be a sin offering. And so he condemned sin in the flesh, ⁴ in order that the righteous requirement of the law might be fully met in us, who do not live according to the flesh but according to the Spirit."

The "therefore" reminds us that what he is about to teach us is directly connected to what he said about life under the Law in Romans 7 and the connection between Law and sin and the result of our "body that is subject to death" (7:24). Paul ends that chapter in the very next verse, 7:25 where he says that the solution to that is deliverance that comes through Jesus Christ.Paul just got things set up for a discussion on the difference between life lived in line with the desires of the Holy Spirit and life lived in line with the desires of corruptible flesh. You see this same distinction made in Galatians 5:16-25 where we find the "fruit of the spirit" contrasted with the life of the flesh,

" ¹⁶ So I say, walk by the Spirit, and you will not gratify the desires of the flesh. ¹⁷ For the flesh desires what is contrary to the Spirit, and the Spirit what is contrary to the flesh. They are in conflict with each other, so that you are not to do whatever you want. ¹⁸ But if you are led by the Spirit, you are not under the law. ¹⁹ The acts of the flesh are obvious: sexual immorality, impurity and debauchery; ²⁰ idolatry and witchcraft; hatred, discord, jealousy, fits of rage, selfish ambition, dissensions, factions ²¹ and envy; drunkenness, orgies, and the like. I warn you, as I did before, that those who live like this will not inherit the kingdom of God. ²² But the fruit of the Spirit is love, joy, peace, forbearance, kindness, goodness, faithfulness, ²³ gentleness and self-control. Against such things there is no law. ²⁴ Those who belong to Christ Jesus have crucified the flesh with its passions and desires. ²⁵ Since we live by the Spirit, let us keep in step with the Spirit. ²⁶ Let us not become conceited, provoking and envying each other."

There are two ways to live in this world - the way that satisfies the desires of corruptible flesh or the way of new life by the Holy Spirit. When you examine the results of each you find they are diametrically opposed to each other...standing in direct opposition to each other. They are mutually exclusive in any given part of life. So when we live by the Spirit we are not living by the flesh and vice-versa.  The Spirit brings life, the flesh death. The Spirit is new creation, the flesh the old man of sin. The Spirit brings light. The flesh brings darkness. The Spirit makes us united. The flesh provokes division.If you look at divisive moments and decisions in the life of the church, you will often see the desires of the flesh at work in what is happening because that is the nature of the flesh. People seeking to find unity in the Spirit are not people who promote division. The Spirit unites but the flesh divides. The Spirit unites because it leads us in a unified direction as a unified people, sealed with and indwelled by the same Spirit. Flesh gives birth to division because the way of the flesh is the way of discord, bitterness, envy, strife, etc which is what results when we seek to fulfill our most base and carnal desires to please ourselves at the expense of others.It is impossible to find unity while trying to gratify the desires of the flesh. It is important that we constantly test our desires to make sure that they are truly in line with the Holy Spirit and not our own selfish, sinful, fleshly desires masquerading as Spirit-led living. Even scripture itself can be used in ways that propagate fleshly desires. The devil did this in Matthew 4 and many Christians have followed suit over the years in using scripture to justify all manner of carnal things.You can always tell what kind of tree it is by the fruit that is produced, which is why I say if you find division you can almost always track it back to fleshly desires. Peter told us that in 1 Peter 2:11, "Dear friends, I urge you, as foreigners and exiles, to abstain from sinful desires, which wage war against your soul." "Sinful desires" is literally "desires of the flesh." These desires, by their very nature bring war not peace and discord instead of unity.

Here is the rest of what Paul wrote in Romans 8:5-13" ⁵ Those who live according to the flesh have their minds set on what the flesh desires; but those who live in accordance with the Spirit have their minds set on what the Spirit desires. ⁶ The mind governed by the flesh is death, but the mind governed by the Spirit is life and peace. ⁷ The mind governed by the flesh is hostile to God; it does not submit to God’s law, nor can it do so. ⁸ Those who are in the realm of the flesh cannot please God. ⁹ You, however, are not in the realm of the flesh but are in the realm of the Spirit, if indeed the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, they do not belong to Christ. ¹⁰ But if Christ is in you, then even though your body is subject to death because of sin, the Spirit gives life because of righteousness. ¹¹ And if the Spirit of him who raised Jesus from the dead is living in you, he who raised Christ from the dead will also give life to your mortal bodies because of his Spirit who lives in you. ¹² Therefore, brothers and sisters, we have an obligation—but it is not to the flesh, to live according to it. ¹³ For if you live according to the flesh, you will die; but if by the Spirit you put to death the misdeeds of the body, you will live."

The other side of the unity of the Spirit is the disunity of the flesh. It is important that we are tune with the antithetical nature of flesh to Spirit so that we can better discern where our desires are truly coming from and be aware of the consequences. If we ever want to achieve unity in Christianity, we are going to have to address our fleshly desires that make unity impossible to achieve.