Why did early humans develop different skin colors

I know it has to do with the amount of sunlight, but the way it happened seems completely illogical. Dark colors absorb more light than brighter colors, that's why they are dark, because there is so little light being reflected back and made visible. On the other hand, light colors have their brightness because they are reflecting back almost all visible light. So if this is true, then why did our African ancestors develop dark skin while our ancestors in Eurasia develop light skin. In a place as hot as Africa, wouldn't you want light skin to reflect the sun's rays and avoid cancer-causing sunburns and heat stroke? And in Europe and northern Asia where the climate is much cooler, wouldn't you want darker skin to absorb as much light as possible? What am I missing?

Exposure to the sunlight causes our skin to secrete melanin, which is a pigment designed to shield our organs from radiation. It has nothing to do with absorbing heat or not. We have other body mechanisms to regulate temperature. The 'natural' color of the original persons skin might have been white because the melanin is likely a protective mechanism that was developed later. Thus, peoples that evolved where the sun is brightest have the most melanin in their skin to prevent the skin from burning and the underlying tissues from being burnt or irradiated. Those not exposed to the sun, from northern climes, lost pigment in the skin because they kept the skin covered all the time and melanin development was lost.

People with darker skin have a decreased chances of burning or developing skin cancer due to sun exposure. People with darker skin, therefore, have a survival advantage over people with lighter skin in areas where there is a lot of sun exposure year round. The people with darker skin, therefore, were able to survive and mate and pass on dark skin genes, leading to whole populations of people with darker skin.