And compared to conventional insecticides, they'll spare more beneficial mites and insects. Another advantage is that they're essentially non-toxic to humans, other mammals and birds. What little toxicity they contain degrades rapidly in the field. Finally, insect pests have not been able to develop resistance to oils because the oils work mechanically to smother adults and eggs. There are with any pesticides.
Oils kill some beneficial insects and mites.
They have no residual activity, so you have to get them right on the pest. They can damage stressed plants. And we've studied them less than other pesticides and so know less about them. On balance though, the advantages substantially outweigh the disadvantages. First, keep the spray mix agitated.