Organic fertilizers actually provide food for beneficial soil microorganisms, while synthetics do not. High or extremely low levels of phosphorus prevent mycorrhizal association with plant roots. Synthetics can produce these conditions more easily than organics because they are soluble and act quicker and do not last as long. That is why organic ferts are considered better for soil life, synthetics are closer to microorganism's waste products and organics are more like tasty food.
Using only synthetic fertilizers is more of a serious problem with big agra, where monocultures and ammonia fertilizer dominate (ammonia is of course anti-microbial). Those fields are very much undergoing depletion and require more and more fertilizer to remain productive because the soil food web dies out eventually. Since P fertilizer is ultimately in limited supply on this earth, and beneficial fungi are specialists in extracting it from the soil it makes sense that we should be building that dynamic for the future of our species. Rather than simply add more fertilizer which now produces more runoff and more red tides and dead zones in our rivers and coastal waters.
Think of the amazon, incredibly lush and supportive of all sorts of life because of masses of rotting organic material and biodiversity producing fertilizer salts for the plants constantly (food web or chain). Remove the plant life and till it and it is productive for a year without fertilizer, then the remaining soil organic material eventually washes away or is eaten by microorganisms without being replaced by the farmer, or in this case, the cattle corporations that supply McDonalds, and desert eventually forms. The synthetics did not do it, but they did nothing to stop it and if an organic farmer were to use that same land they would use cultural practices to try and make the land sustainable by decreasing erosion and adding back organic material to the soil.
I do not use synthetic fertilizers because of the big picture, I cannot support something so disgusting and dangerous, even if my small usage is basically harmless in comparison. I gave up meat shortly after getting out of the army because it causes so much land destruction. I had just got done with my tour of Baghdad, the birthplace of agriculture and now a barren dustbowl because of many centuries of Organic-over-farmiing. Or society today can accomplish the same much faster.
Of course I do not hold it against any of you fellow figgers, you never razed hundreds of acres of virgin forest and caused extinctions which could have cost our society cures for diseases so you could win some short term personal gains by growing cheap beef. You are using the fertilizer because you love your trees, and I can respect that.