This paper investigates the impact of antenna correlation on full duplex massive multiple-input multiple-output ( MIMO) two-way relaying systems. To be general, all nodes in the system are equipped with multiple antennas and arbitrary antenna correlation is considered. Deterministic equivalent of the achievable sum-rate is first given, which enables the derivation of the asymptotic sum-rate when the number of relay antennas is large. The impact of antenna correlation on the asymptotic sum-rate is then thoroughly analyzed. The results reveal that with a large number of relay antennas, the asymptotic sum-rate is independent of the antenna correlation at the relay's transmitter side, however it is Schur-concave with respect to the eigenvalue vectors of the involved antenna correlation matrices at both the users' transceiver sides and the relay's receiver side. In other words, the antenna correlations at both the users' transceiver sides and the relay's receiver side have detrimental effects on the sum-rate. Moreover, the antenna correlation at the users is more significant to the asymptotic sum-rate than that at the relay. The analysis is general and can be easily reduced to consider half-duplex and/or one-way massive MIMO relaying systems. Numerical results are finally provided to validate the analysis. It is also shown that a larger number of user antennas may not always lead to a higher sum-rate, and thus proper selection of the number of user antennas is necessary to maximize the sum-rate.