Not much is mentioned about who Chloe or Chloe’s people are (yet) outside of them being in relation to the family name who would have been people who were possibly other believers that were concerned with divisions and dissension among the fellowship of believers.
The fact that there needs to be a reporting of rivalry is a reflection of many things that goes on and is supposed to go on in the Body of Christ because:
1. Some unbelievers are among believers
There are going to be wheat (sheep of God) among the tares (lukewarm and not saved yet or are children “seed” of the devil) in any fellowship so this will cause rivalries as mentioned by God to be the case back in Genesis 3:15 where God said to Eve that her seed (Jesus) would be at war/enmity with the serpent’s seed (followers and children of Satan) and this is because the righteous who follow Christ are not in union with the wicked who follow the devil but are in union with Jesus who is in opposition to the devil as the light opposes darkness. But much is learned on how to act and how not to act by having the wheat among the tares together for a time which is why I believe is why Jesus states to leave the tares alone in Matthew 13:24-30.
2. Spiritual meat is not digestible when you’re on a current diet of spiritual milk
Rivalries will happen even among believers because while we are all learning to unlearn the ways of the world and the works of the flesh through faith in Jesus we are all going to be at different stages of growth on our walk with Christ which means different levels of understanding and maturation is going to be present which is going to lead to sometimes causing someone who is spiritually immature to not agree with something someone who is spiritually mature says and does because of them not being able to yet comprehend something that Jesus has yet to teach them or because of not being able to ingest the meat of a teaching because they would have yet been weened from the foundation of the milk that is required to ingest in order to fully agree and understand spiritual meat. This is why we are to be gentle in giving wisdom from our Father above because we are also allowing for what is given to be readily received and accepted.
3. The desire to be “right” usually outweighs the desire to learn in the moment when pride is in the way
This is seen in the following verses where Paul is correcting the people who are boasting about who they are “of” and likely who they were baptized by as a way to say they are better than another believer because of who baptized them and who they were taught by.
This can happen amongst believers and amongst people who are not of the faith but who are also believers in Jesus.
This is heavily seen through religious debates where regardless of what religion someone is professing they are most of the time more focused on being “right” in an apologetic debate over sharing the righteousness of God and this leads to both parties (whether right or wrong) to not learn and retain the knowledge and wisdom of God (if He was mentioned in the debate/conversation) all because the flesh and pride would have been in the way.
There are likely more reasons why there are rivalries in the present-day church or at the church of Corinth but these were the first that came to mind.