I'll take a stab at this, with the caveat that this is a conversation best done in person and that there is a lot of history involved and that these are my PERSONAL opinions (not indicative of any group or organization within the SCA, Calontir, etc, etc, etc).
The arguments are many varied depending on who you talk to. For me, the strongest question/argument I have is: Why does rapier need a peerage when equestrians and archers, also martial activities, don't have one?
What makes rapier different from other studies/activities such that it deserves its own peerage? As it stands, recognition at the Peerage level is granted under Arts and Sciences (the art of fighting, the science of warfare, etc). You become a rapier laurel, equivalent to an equestrian laurel or archer laurel or costuming laurel or cooking laurel.