In this paper, the performance of full-duplex (FD) two-way massive multiple-input multiple-output (MIMO) relay systems is analyzed. One popular linear relaying scheme, i.e., maximum ratio combining/maximum ratio transmission relaying, is particularly investigated. Different from prior analyses, multi-pair of MIMO users and antenna correlation at both the relay and the users are considered. Asymptotic sum-rate under a general case is first derived. Four special power scaling cases are then discussed and the corresponding asymptotic sum-rates are derived in simple forms with clear insights. The analytical results clearly quantify the impacts of self-loop interference, intra-group interference and antenna correlation, and discover the power scaling laws under various cases. It is found that the transmission powers at both the MIMO users and the relay can be scaled down inversely proportional to the number of antennas at the relay while maintaining a desirable sum-rate when the number of antennas at the relay grows large. The FD two-way massive MIMO relay system is finally compared with the half-duplex (HD) counterpart. It is revealed that under two special power scaling cases, the FD system can achieve double sum-rate when compared with the HD system. However, under the other two power scaling cases, self-loop interference and intra-group interference degrade the asymptotic sum-rate and the FD system may perform worse than the HD system. The maximum allowable self-loop interference for the FD system to outperform the HD system is given explicitly. In addition, the impact of antenna correlation at the users and the relay is analyzed. The results show that the antenna correlation at the users has complicate impact on the sum-rate, while the antenna correlation at the relay may not affect the sum-rate under certain power scaling cases.