Cooperativity is an important and ubiquitous concept whose origin is still not well appreciated. Using the new quantitative measure of this concept that we recently proposed, in this work, we investigate the origin of negative cooperativity for two ionic systems, either a lithium cation or fluorine anion embedded in an argon cluster with up to 20 argon atoms. This measure is found to be strongly correlated with thermochemistry quantities like enthalpy and Gibbs free energy. Dependences of negative cooperativity on density functionals and basis set are examined. Two energy decomposition schemes are employed to investigate the origin of the cooperativity effect. Quantities from the information-theoretic approach have also been utilized to pinpoint the origin. We find that the characteristics of negative cooperativity for ionic clusters is its strong correlation with information gain and Renyi entropy, which are closely related to nucleophilicity, nucleophilicity, and quantum entanglement. These results should shed new light in appreciating cooperativity effect and its impact on chemical reactivity in many chemical and biological systems.