What are A and B antigens? What other effects do they have? And why do they exist?

Your body's immune system is scrupilous in its elimination of B cells that are reactive to self antigens. If a person has these "A or B antibodies" then their B cells are reacting against "self" antigens and producing antibodies against self cells. This would be considered an autoimmune disease. These antigens are your cell's surface markers so that other cells in the body know that 1. the cell belongs to you (or sometimes it only thinks that in the case of blood transfusions) and 2. that it is a red blood cell. Every cell in the body has "self" antigens on its surface that indicate to macrophages and neutrophils that they are not foreign. They are like cellular name tags, that way immune cells can better keep track of cells that do not belong in the body. Technically, only people with type A blood who have been exposed to type B blood should have B antibodies, and vice versa. Naturally, no person should have A or B antibodies within their bodies.