That isn't how technological evolution works. Despite what Sid Meier would have you believe, "Stone Age", "Bronze Age", etc. are not fixed, universal stages of development. They're terms of convenience that archaeologists use to refer to periods based on their dominant artefact type, and very roughly date them in the absence of more precise, scientific evidence. The system was developed in Europe to fit European prehistory, and while it was found to work well enough (with modification) in a few other regions, it doesn't apply everywhere. Notably, it's useless for classifying New World prehistory, and American archaeologists use a completely different periodization. That's because technological evolution is highly nonlinear, culturally specific and historically contingent – it never takes quite the same path. In other words, this question is kind of like asking, "European civilisation was politically fragmented, so why didn't they advance into the Tokugawa shogunate?"

As for your question about why New World societies didn't develop bronze or iron metallurgy, I'll point you to this section of the FAQ, because it's been answered many times by much more knowledgeable people than me. The short answer is that while copper was used extensively, the Americas didn't have any deposits of copper and tin in close proximity, and so bronze wasn't practical. As a consequence, metallurgy was never as useful or widespread in the Americas as in the Old World, because they were stuck with soft metals (copper and gold). Similarly, American metallurgists made use of native iron, but native iron is very rare, and they didn't have the high-temperature smelting technology required to extract iron from ores. Eurasians stumbled onto this technology somewhat obliquely: they developed kilns early, to make decorative pottery, and found a reason to stick with it to extract lead and tin. Americans didn't go down this route, and so were never in a position to apply it to extracting iron ore.