To start with, I think, perhaps even a better question is why wouldn't you grow your containers organically? Given all the information available, on a common sense basis, given a choice, why would you want to ingest foods that have been grown using chemical fertilizers and pesticides? One of the primary beauties of growing your own food is that you can control what goes into it and given that control, and that it is as easy and potentially safer to eat foods that are pesticide free, why wouldn't you grow organically?
For me the reasons to grow my plants organically are many. I believe that growing food sustainably is a goal that is important and I believe that, particularly when gardening on a small scale, we can just as easily garden sustainably and can minimize the use of chemicals and pesticides as well as chemical fertilizers. I don't think there is any reason, in small scale gardening, container or conventional, to use pesticides or chemicals.
While you can find lots of studies that argue both sides of the nutritional benefits of organically grown vegetables, there seems to be agreement that produce grown organically, has a higher percentage of vitamins and phytochemicals. Organically grown produce can contain as much as 40 percent more antioxidants than conventionally grown produce. While some say that there are no proven benefits to eating those antioxidents, again, why wouldn't you want food with that potential upside, with no downside?
Though many people would disagree, I believe that edibles taste better when they are grown organically. There is also mounting evidence to support that claim. In a recent study, when rats were given the choice of eating biscuits made with organic, versus conventionally grown wheat, they ate substantially more of the organic biscuits.
In addition, (playing the devil's advocate here), even if it is only my perception that the food tastes better, that in a blind taste test, I might not know the difference, and the perception that the food tastes better is the result of a placebo effect (I think the food tastes better so therefore it does), I still enjoy it more!
In addition, there is evidence that growing your container gardens organically, is less expensive and less work. According to Pete Bottomley, of Coast of Maine, makers of organic garden products, until about five years organics were more expensive. Now it is actually cheaper to do organic vegetable gardening.
Another important factor in my decision to garden organically is that I don't want to store poisonous chemicals or pesticides in my home. While my children are now too old to ingest dangerous chemicals, my pets are still at risk, as are visiting children.
Another huge advantage of using organics is that it feeds the beneficial micro-nutrients in the soil. While a fertilizer like Miracle-Gro will work and adequately feed your plants, it will kill all of the beneficial micro-organisms in your soil.
It is obviously your choice whether to use conventional fertilizers and pesticides, but I would encourage you to at least give organic gardening a try.