Demixing phenomena in the aqueous solutions of organic molecules are considered due to the temperature induced structural changes of the hydrogen bonds between water and organic molecules. The lower and upper critical solution points are attributed to the appearance of the "critical" concentration of the complexes with one hydrogen bond between a single water molecule and single solute molecule. Namely, the hydrogen bonded pair complexes are responsible for the formation of the strongly associated water clusters around solute molecules that may be followed by separation of the homogeneous solution on water-rich and organic-rich phases. The extension of the immiscibility gap upon strengthening of the hydrogen bonds between water and pyridine is obtained. Experimentally observed changes of the lower and upper critical solution temperatures upon the deuteration of water, addition of salts, and presence of the alkyl substituents in the solute pyridine molecules are well reproduced in the framework of the proposed model.