
It is mainly to prevent undesirable people from joining.
Puppy farmers for example wouyld be able to add credibility to their breeding if they say they belong to a breed club. People are more often now told that anyone who is serious about their breed belongs to one or more breed clubs.
Most breed clubs including my own have a proposer and seconder, but the applications go through on just me proposing my new puppy owners, and as Jackie H says trying to ascertain that there is no known reason to not accept them.
It is much harder to remove an undesirable person from membership of a club, than to prevent them joining in the first place. Most people know someone in their breed that is a member of their chosen or another club. If you go to a club event you can usually find someone who will propse and second you if you Introduce yourselves to committteee members and explain you wish to join.
Most mebers ofour National breed club are Pet owners. they are usually proposed by the breeder of their pup, and sometimes seconded by the Stud dog owner.