Why is partial pressure proportional to mole fraction in Henry's law?
1st, Henry's law of Partial Pressure states:

&quot;At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.&quot;

Quoting from WikiPedia here:

Henry's law is a limiting law that only applies for 'sufficiently dilute' solutions. The range of concentrations in which it applies becomes narrower the more the system diverges from ideal behavior. Roughly speaking, that is the more chemically 'different' the solute is from the solvent.
For a dilute solution, the concentration of the solute is approximately proportional to its mole fraction $x$, and Henry's law can be written as:

$$p = K_{\rm H}\,x$$
,where $p$ is the partial pressure of the gas above and in equilibrium with the solution, and $K_{\rm H}\,$ is the proportionality constant called the Henry's Law constant.
This is a conceptual conclusion as steeper the concentration gradient, the rate of diffusion (and hence the amount of diffused substance) will be greater. Here, the concentrations of the &quot;solute&quot; is represented by partial pressure of the gas in the gaseous state and by it's corresponding mole fraction in the solution state.
What you have supposed stands only for a closed system. As in the second quote from WikiPedia, you understand that the law is applicable only for conditions in which the behavior/condition which you supposed is either not relevant or is negligible.
If you go through the linked article, you'll find that Raoult's Law for Vapor Pressure of Solutions appears to be a special case of Henry's Law for more concentrated solutions, and can be used as such.
Note that both Raoult's Law and Henry's Law are limiting laws and they are applicable each as when:
Henry's Law: $x$ → $0$
Raoult's Law: $x$ → $1$