Some organic pesticides are dangerous. These seem to mostly be problematic when natural ingredients are industrially concentrated. Also, seems some companies sell synthetics that can be derived from plants, but aren't for economic reasons, and still call them "organic". (Personally, I think calling an substance derived from plants but which is extracted with a number of synthetic and toxic chemicals is kind of stretching the meaning of the term 'organic' to the breaking point).

There are many that are much more safe: neem oil, citrus oil, tobacco, salt water, baking soda water, chili powder, soap.

I think that the presumption of danger from pesticides derived from plants humans have been living alongside for millennia should be less than novel synthetics that may have only existed for a decade or two.