I'm skeptical of the health benefits of organic food, and yet another meta-analysis of organic food health benefit studies confirms this skepticism. This is a concern because a lot of organic consumers are motivated by a desire to enhance their own health and pay a high premium for this benefit which is marginal at best and may not exist at all.
I do think that there are plausible arguments that organics may make sense for vulnerable populations (e.g. pregnant women), although good food cleaning and cooking high risk foods may be a good substitute.
The stronger claim for the usefulness of organics are environmental and macro-level. Synthetic pesticides and fertilizers can cause dangerous and (intentionally) little regulated toxic pollution in runoff. It can harm farmers and those around farms. It can harm the health of those downstream from them. The most vulnerable populations to these toxins are not humans, who drink scientifically treated water and live mostly far from the places where food is produced, but wildlife (on land and water and in the air) and plants.
Fertilizers, and the fuels required by heavier use of machinery in conventional farming, are petroleum intensive. This makes conventional farming part of the oil import problem, holds food prices hostage to oil prices and is unsustainable in the long term. Organic farming critics argue that the energy intensive nature of conventional farming is compensated for by its high per acre yields. Higher yields may imply that energy use is not as intensive per output as believed.
Higher yields per acre also mean that organic farming has a bigger footprint for its output, that impinges on wild habitats, compared to conventional farming. In this view, organic farms are the exurbs of agriculture.
The environmental claims are different in kind, so both sets of claims could be true. Moreover, organic farming has such a small market share that acreage isn't a big concern at this point, which is beyond the experimental stage, but is still very much an R&D stage niche enterprise. Organic farming is to conventional farming what hybrid cars are to conventional cars.