We present a detailed analysis of the upper critical field for CeCoIn5 under high pressure. We show that, consistent with other measurements, this system shows a decoupling between the maximum of the superconducting transition temperature T c and the maximum pairing strength. We propose a model in which, in order to account for the discrepancy in pressure between the maximum of the upper critical field and the maximum of T c, we introduce magnetic pair-breaking effects, already widely suggested by other measurements. We found that within the Eliashberg frame work, the unusual shape of H c2(T) can be completely reproduced when magnetic pair breaking is taken into account. Surprisingly, we found that the maximum of pair breaking and of pair coupling coincide in pressure, suggesting that both mechanisms originate from quantum criticality. Our model implies that CeCoIn 5 is the first compound of its family that shows clear decoupling between the maximum of T c and quantum criticality.