A family has a tangible existence. Its members actively interact according to established protocols. A team also has a tangible existence. Its members also have active relationships. A social class has no such tangible existence. It is merely a mental construct to aid perception. Why then is it so divisive?
The human life-form exists in a wide range of different sizes, strengths, shapes, features, skin colours, ideas, beliefs, traditions, aspirations, preferences, interests and other observable characteristics. The human mind tends to perceive an individual who has a particular characteristic as being a member of the set of all individuals who also have it. Hence any individual with the physical characteristics of black skin and curly hair is perceived to be a member of a set which is called the Afro-Caribbean race.
The mechanisms of human perception thus tend to classify society into unconnected overlapping classes such as race, ethnic group, school of thought, religious church, political party, trade or profession, economic class, sporting fraternity, or any groups whose members share common interests or attributes. But classes are not simply large teams. Being a member of a given class does not of itself mean that you will have any interaction with all, or even some members of that class. You simply — and probably entirely co-incidentally — share one or more common characteristics with your fellow members.
Being a member of one class does not exclude you from others. On the other hand, a fellow member of one class to which you belong may not necessarily be a member of another class to which you belong. An individual can at the same time be a member of the Afro-Caribbean race and a member of the Institute of Mathematicians. But not all members of the Institute of Mathematicians are members of the Afro-Caribbean race.
A class of which you are a member is, however, a place where you are likely to find soul mates with whom you could form a balanced team. You would look for members of a class to which you belong who also belong to classes likely to have the skills you are lacking for your team. It is for this reason that members of certain classes set up membership administrations and become clubs or institutes with organised meetings.
There is a class of human life-forms who have the geographic attribute of living in the British Isles. By default of mutual proximity, they share many other attributes also. Because they share things in common which distinguish them from the myriads of other humans on this planet, they are perceived as a separate class of humans known as The British. I am British. I have relationships with a small number of others who are also British. I also have relationships with people who are not British. But I have no active relationships at all with most other British people.
Being a member of a team implies that you interact intensely with other members of the team to achieve a defined tactical objective. The team has a tangible existence and can exert an effect on its environment. But being a member of a class means only that you happen to share particular features with the other members of that class. The class itself has no tangible existence other than as an aid to perception to help an observer to differentiate and understand certain characteristics of human beings.
Why is social class so divisive? Why is one social class so often the focus of another's hatred? Why do members of one social class automatically despise those of another? The many are subject to the few. The few inflict stress and deprivation on the many. The many bemoan and resent their condition. They need a focus for that resentment. The few who cause it are too powerful. A weaker scapegoat is required. A different social class — especially a minority one — is the most convenient. The oppressed many therefore heap upon it the hatred they should rightly visit up on their elite oppressors.