The COVID-19 pandemic showcased a coevolutionary race between the human immune system and SARS-CoV-2, during which the immune system generated neutralizing antibodies targeting the SARS-CoV-2 spike protein's receptor-binding domain (RBD), crucial for host cell invasion, while the virus evolved to evade antibody recognition. Here, we establish a synthetic coevolution system combining high-throughput screening of antibody and RBD variant libraries with protein mutagenesis, surface display, and deep sequencing. Additionally, to significantly extend our interrogation of sequence space, we train a protein language model that predicts antibody escape to RBD variants and demonstrate its capability to generalize to a larger mutational load and mutations at positions unseen during training. Through explainable AI techniques, we probe the model and identify biologically meaningful coevolution trends. Synthetic coevolution reveals antagonistic and compensatory mutational trajectories of neutralizing antibodies and SARS-CoV-2 variants, enhancing the understanding of this evolutionary conflict.