Reasons to use symmetric encryption in your case:
It is way faster then asymmetric encryption
Asymmetric encryption is quite expensive when it comes to computing time.
You already have everything in place to use symmetric encryption.
You are distributing Private Keys anyway so why not just distribute a symmetric key.
Asymmetric encryption is not well ...
Yes, there's a reason; public key encryption is very slow and CPU-intensive, and not at all suitable for encrypting chat data, which may well include images, audio or video as well as text. That's why wherever it's used, it's only used to transmit a shared symmetric encryption key which is then used to encrypt the actual content. But in any case, it's never ...