Why is the boiling point of homologous primary > secondary > tertiary alcohols whilst their solubility in water is the reverse?
The key concept here is that for solubility, you need to compare alcohols with the same number of carbon atoms. For example, the solubility order of isomers of butanol is as follows:
$$\ce{CH3CH2CH2CH2OH &lt; (CH3)2CHCH2OH &lt; (CH3)3COH}$$

This difference in solubility follows the order 3°>2°>1° and can be explained by the branching concept that you have used in your question. However, If you compare alcohols with different number of carbon atoms, say butanol and methanol, then the alcohol with a smaller hydrocarbon part will be more soluble in water. 

The boiling point of alcohols increases with the increase in the number of carbon atoms, as stronger van der waals forces start acting in between the molecules. For example, Phenol boils at around 180°C whereas methanol boils at around 60°C. For alcohols with the same number of carbon atoms, a more exposed hydroxyl group will result in stronger intermolecular H-bonding.

TL;DR: your comparision can only be applied for alcohols with the same number of carbon atoms