A group wants to change the protocol, the other doesnt want to. Since the BCH network isnt owned by anyone, any group of people with enough hash power can fork the network and coexist with the previous chain.
No one can say what will be the price.
Thank you for your explanation. "A group" here means people runs BCH nodes and mines BCH?
basically a fork is a change of rules in a cryptocurrency system. so the other reason that you asked above about forking BCH is to change consensus rules.
now to do that you need the network to accept the change and upgrade to the new software that implements that change. the network consists of miners (providing hashing power) and nodes (the backbones of the network enforcing the rules) so you need them to upgrade.
such changes however will require a high amount of support. so a "group" in this context can not be a couple of miners who have 1% of the total hashrate. which is also why "bitcoin" defines these hashrate support thresholds for each fork (>95%).