Antibodies are produced by the body in response to foreign substances, called antigens. The venom of a snake is an antigen. The body will respond and produce antibodies. However, the production of antibody takes weeks, and someone can die from the venom before any antibody can be produced. The antivenin were produced by injecting horses with snake venom, and horse blood is then drawn to extract the antibodies. If a snake bite victim is given antivenin, it will neutralize the venom so that there is virtually no venom left to stimulate the production of antibodies. There are some snake owners who inject themselves with minute amounts of snake venom to build up immunity. It is doubtful that a snake bite victim treated with antivenin will have enough venom left in their bodies to produce antibodies. It is certainly possible, but it would be foolish to fhink that once bitten then you are immune. It is better safe than sorry. Besides, different species of snakes have different kinds of venom. Therefore, in order to be immune, a lot of different of antibodies are needed.
Some people are allergic to horse serum, but they are still treated with antivenin because the snake venom is worse than any allergic reaction to the antivenin.