I think that Charlie is trying to get Parson to fight Fate, because he can't do it himself.
I like to think that carnymancy is tied somehow to what someone believes, or by hook or crook what you can make them believe; an audience-based magic. It might explain why Sylvia thought she could not croak, if that belief through carnymancy could be made manifest into an actual effect in a cart-before-the-horse scenario. This is a real stretch, but could even explain something visually silly like Stanley only sometimes turning walnuts into pigeons, as he is a terrible showman, or Van de graff looking like something that can hurt you actually becoming something that can hurt you. For a more recent example, Jojo asking Parson what he believes and telling Parson that you can fight Fate and win could be a set-up, and requirement, for the use of the scroll. If this is the case a master-class carnymancer would probably set the limits of the discipline on their ability to sell it, and we have seen silver-tongued Charlie sell everybody on everything. Fooling yourself won't do any good, so you need to fool somebody else into doing something Impossible, like Dumbo and his magic feather, with the difference being that carnymancy can make something you believe into something real, as opposed to you already being able to do it.
However, this may be reading into mechanics too much. A simpler story-based explanation is that a Perfect Warlord such as Parson might be capable of leading any engagement, which would include against Fate (or War) itself. Whether Parson is there to directly fight Charlie or not, Charlie would prefer a scenario where he can use Parson to his advantage as opposed to getting rid of him. It is still unknown at this point what Charlie knows about Parson or any predictamancy that Parson may be fulfilling. Also we don't know if Charlie is aware of the conspiracies against him, or if he simply maneuvers as though everyone is out to get him already.