Question

why we write C for carbon and Co for cobalt

Answer 1

Its based on The Latin names. But not only that it depend on the IUPAC conventions also. So It was the only symbol suitable for these Elements Cobalt and Carbon.And also were arranged in a dictionary order.In the for of comparison with each element

Answer 2

We write C for Carbon Because in some element the symbol of the element is taken form its first words and Co for Cobalt beacause in some elements the symbol of the element is taken from its first second letters, so that the we don't get confuse.