That would be a good reason to consider conventional. Both organic and conventional farms use pesticides. But, by restricting themselves to only pesticides that a program within the USDA's Agricultural Marketing Service has deemed are sufficiently "natural" (not safe, not effective, not environmentally friendly, just natural), they're often limited to using chemicals that are less specific, don't break down as well, or rinse off more easily than the best available options.
Less specific means they're more capable of harming you (and wildlife in general) instead of just the target species. Breaking down less well means they're more likely to remain in the food. And rinsing away more easily means that they're more likely to pollute the soil and groundwater, and also that they may need more frequent application.
The crux of the problem is, the basic idea behind organic standards tacitly bans engineering. And by banning engineering, you ban all engineering, including engineering things to be safer, cleaner, or more effective.
I don't want to get into whether our current standards governing the safety of agrichemicals are perfect or not. What I want to suggest is that the USDA Organic program doesn't effectively improve on that situation. Conventional and organic products both have to meet the same bottom line. By introducing an additional restriction that has nothing to do with safety, though, organic farming hasn't self-imposed a higher minimum standard. It's unnecessarily self-imposed a lower maximum standard.