How is Raoult's law a special case of Henry's law and not vice versa?
Raoult's law is a proposition regarding the relationship between the vapor pressure of a solvent (component 1 below) in its pure form ($p_1^\circ$) and when a solute (component 2) is present at a mole fraction $\chi_2=1-\chi_1$ (the vapor pressure then $p_1$):

$$\chi_1 = \frac{p_1}{p_1^\circ} $$ 

It is generally true for very dilute solutions because we know independently that

$$\frac{p}{p^\circ} \rightarrow1 \,\, \text{as} \,\,\chi_1 \rightarrow 1$$ 

For some ideal binary systems Raoult's law is applicable over a broad range of composition. In fact, sometimes the solute also observes Raoult's law in dilute solutions:

$$\chi_2 = \frac{p_2}{p_2^\circ} $$ 

This however is exceptional behavior. It is more common that the solute observes the general Henry's law

$$\chi_2 = \frac{p_2}{K_H} $$ 

where $K_H$ is a proportionality constant for the solute-solvent pair. It should be evident that when $K_H=p_2^\circ$ the solute displays Raoult's law behavior even in dilute solution. 

Henry's law is a general statement observed by solutes with a measurable vapor pressure $p_2$, since the following limiting behavior is expected as solute-solvent interactions far exceed solute-solute interactions in importance in the limit of zero solute concentration:

$$\frac{p_2}{K_H} \rightarrow1 \,\, \text{as} \,\,\chi_1 \rightarrow 1$$ 

However, there is no principle that guarantees that $K_H=p_2^\circ$. Again, for a substance to follow Raoult's law at low concentrations is regarded as exceptionally ideal behavior.