Taking the long view, asexual organisms tend to accumulate mutations over time in a process known as Muller's ratchet. Sexual organisms, because they mix genes around, tend to let bad mutations slip out of the gene pool. This is one possible benefit of sexual reproduction. Parasites attack other organisms. The first step of this attack is to attach to the victim's cell wall and then burrow in to the sweet cytoplasm inside.
Parasites evolve mechanisms of detecting and attaching to the cell walls of hosts.
This evolutionary process is much more effective when the hosts' cell walls are stable over time. If the cell wall changes frequently, then it makes parasitic evolution all the more difficult. In asexual organisms, each individual shares the same genes for the cell wall, so parasites have it easy. With sexual organisms, mixing of genes means that each offspring has a different set of genes, and so each individual may have a different cell surface. This makes it much harder for parasites to evolve effective invasion techniques.