Jealousy and strife are two of the “social sins” that Paul mentions in Galatians 5:19-21 — enmity (hostility), strife, jealousy, fits of anger, rivalries, dissensions, divisions, and envy. These deeds of the flesh are in direct opposition to the fruit of the Spirit (Gal 5:22-23). In fact, Paul says that the two are “against” each other (Gal 5:17).
This is relevant to the Corinthian church because they claimed to be “spiritual” people: believers who had progressed in wisdom and maturity such that they could challenge even Paul. He affirmed that they were believers, calling them “saints” and “brothers” and acknowledging that the testimony of Christ was confirmed in them due to the gospel coming in a “demonstration of the Spirit and of power.”
But Paul says that their claims are inherently contradictory. Something that they were doing was so contrary to the gospel, so contrary to the Spirit, so contrary to the cross of Christ, that he could not consider them “spiritual” in his instructions to them, but instead had to treat them as “fleshly” and “infants” in Christ. He says that they are being “merely human.”