My first response it to think about the law of large numbers. Generally speaking, as the number of risks gets larger, even if the exposure to them is lower, the insurer can more accurately estimate their total claims for a period and thus improve the predictability of their experience.
However: the aim of reciprocal quote share reinsurance is to diversify your risks, like Akani said. Two insurers would enter into an agreement to share their claims - they may be sharing the same insured risk (e.g. motor insurance - see Rowan's answer from last year here) but just now across a more diverse group of policyholders, e.g. geographically or by other factors. They could also be sharing different risks - exchanging a portion of a life insurance book for a portion of a motor insurance book.
The amount of capital the insurer needs to hold also decreases as diversification increases.
You asked about the process that takes place:
The two companies entering into the agreement will come up with their own terms - they would swap a portion of the book such that the size of the risk ceded and the risk accepted are equal, i.e. the expected liabilities are the same for both parties. (See Landi's answer from 2017 here - she says that alternatively, both could decide on a premium to charge each other for taking on a portion of the other's risk.)