Fights on facebook are generally not worth it... Even if you "win" you end up looking like someone who is spoiling for an argument (even if that's not true).
FWIW, I got into a similar conversation with someone recently. Basically I told them that if their view (only shelter dogs should be adopted, no breeding) was actually made reality, we would no longer have any dogs because all shelter dogs are sterilized on intake. Their argument was that "dogs exist for their own purposes and it is wrong to control their lives for our own purposes." I then asked them if their real problem was that people own domestic animals at all, and if their agenda was to abolish pet ownership. Silence.
I usually try to make it clear to people that "dog breeders" are not just one thing, and that people breed dogs with a variety of different agendas, not just to make money or as a status symbol. Most are also not informed at all about working dogs vs. show, or small hobby breeders vs. BYB vs. puppy mill (understanding that these things do not have clear definitions). I then try and point out that it is best to learn as much as you can about something before saying it should be forbidden under any and all circumstances.