For many types of genetic analysis you need to look at many different embryos at many different stages to understand what the problem is with a given mutation. The embryos develop outside the mother's body , so you can have easy access to them. In contrast, mouse embryos develop inside the mother, and you have to kill the mother to get at them. This would have to be done at each of the stages of development you want to look at. Once you do this, of course, the embryos die as well as the mother, so you are very limited in the types of experiments you can do.
Zebrafish embryos are transparent .
This means you can watch development as it happens in living embryos. You can see internal organs, such as the brain, heart, blood, muscles, etc. It is not possible to achieve this resolution with other systems. The embryos develop quickly . They go from a single cell to something that is recognizable as a tiny fish within 24 hours.