"They are simply a person from conception" sounds like a definition to me, nothing to to with the capability to argue. "The actual act of arguing is not necessary to qualify as a person, just the capability to": babies don't have the capability, just "the potential" to argue at some unspecified point in the future, which is enough to make them rational beings and therefore persons? So the sperm and ovum, even before having fused, are also a rational being, having the "potential" to argue at some point in the future? That would not only make abortion a violent act, but also not having sex.
Also, babies born with a mental handicap, not having "the potential" to grow into a rational being, can be kicked to death without further ado? Or a they "persons" by some other convenient definition? "May have had the potential of eventualy becoming a rational being"?
You would also have to prove that chimpansees are not rational beings even though they show rational behaviour and even engage in non-violent (and non-verbal) arguing in stead of just defining them as non-rational beings.
I think this line of reasoning is a dead end when it comes to investigating animal rights.