Why do some organisms use both types of reproduction?

is faster but leads to more mobile adults and a hardy egg stage.

Using the example of Aphids (plant-sucking insect pests):

Many Aphid use both asexual and sexual reproduction.

Asexual reproduction has the benefit of being very rapid. One aphid can cover an entire plant very quickly without mates - they give birth to live young. Constantly.

Why use sexual reproduction? Well, of course, sexual reproduction involves the mixing of DNA from two individuals, so the population will have more genetic diversity. So if there is a disaster, like a disease or the host plant dying, some individuals will have a slight edge to survive and reproduce.

But in the case of Aphids, sexual reproduction has another advantage. While asexual reproduction is carried out by giving birth to live young (strange for an insect), sexual reproduction results in the laying of eggs.

In Aphids, eggs are very hardy structures. For some species, that is the only way they can survive in winter because all the adults are killed off from the cold. When the eggs hatch, the aphids will begin asexual reproduction and the cycle begins again.

As another benefit for Aphids, the individuals that do the sexual reproduction are winged. This allows them more mobility to find mates, spread to new plants, and, critically, to switch host plants. Some species begin on one host species and then, generations later, switch to another host species.