Movable antenna (MA) provides an innovative way to arrange antennas that can contribute to improved signal quality and more effective interference management. This method is especially beneficial for co-frequency co-time full-duplex (CCFD) wireless communication, which struggles with self-interference (SI) that usually overpowers the desired incoming signals. By dynamically repositioning transmit/receive antennas, we can mitigate the SI and enhance the reception of incoming signals. Thus, this paper proposes a novel MA-enabled point-to-point CCFD system and formulates the minimum achievable rate of two CCFD terminals. To maximize the minimum achievable rate and determine the near-optimal positions of the MAs, we introduce a solution based on projected particle swarm optimization (PPSO), which can circumvent common suboptimal positioning issues. Moreover, numerical results reveal that the PPSO method leads to a better performance compared to the conventional alternating position optimization (APO). The results also demonstrate that an MA-enabled CCFD system outperforms the one using fixed-position antennas (FPAs).