The main two reasons why the Kyoto Protocol is controversial are the economic justification, and the non respecting of it by some countries.
The amount of time predicted for the countries to reduce the CO2 emissions in the atmosphere by converting to other natural resources for energy is very small. The large economies can not convert so quickly from one natural resource to another as their economies are massive and all based mainly around one or two natural resources for energy. The conversion itself also seems to not be economically justifiable as it requires enormous investments.
The two biggest economies and emitters of CO2 into the atmosphere, the USA and China, do not respect this protocol, and they are responsible for almost one half of the global emissions of this gas. And it is not just these two, but numerous countries that signed the protocol do not respect it in practice, especially when it comes to the developing and less developed economies.