Why do archaeologists mark time periods by the kind of material used for making tools?

Because we are talking about prehistoric times which means that no written information by or about peoples is available. As soon as it is, archaeologists mark the periods as for instance 'the 24th dynasty' or 'during the reign of king Hammurabi'. Until then, the development of peoples can only be measured by the artefacts and tools they left behind. And we do know that the sequence in time always was stone - bronze - iron.

It should be noted however that the stone age etc. is not either a universal of specific period in time. One people could be in the iron age while a few hundred miles away others could still live in the bronze or stone age. For some peoples the stone age ended only in the early 20th century.