Your bodies response to a virus makes it difficult for another virus to take hold, but not impossible. There's a lag in the body's immune response when a virus

Your bodies response to a virus makes it difficult for another virus to take hold, but not impossible. There's a lag in the body's immune response when a virus first is detected, and then another lag while the body builds up the defenders (antibodies and other things). So for someone to have multiple viruses at the same time, largely the exposure has to happen at the same time. The more different the viruses are, the more likely they can be in the body at the same time in a meaningful number. When an immune system is "all revved up", it is very hard for a few thousand virus cells to get exponential growth going needed. Antibodies (and b-cells and t-cells) for Delta work ok enough against Omicron, and vice-versa. Since Omicron is spreading so fast, it is able to get to more bodies faster than Delta, so Delta has no where to go. Delta did the same to previous variants.