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Resistors only drop voltage if current flows through them and the amount dropped depends on the current. Assuming your load draws zero current, which is a good approximation of most voltage inputs (which your Vout feeds into), without R2 no current flows through R1 so no voltage drops across R1 so the voltage on both sides of R1 are the same.
The role of the second resistor is to provide the current... It is also interesting to replace it with a current source...
That’s what all the other answers fail to point out: A voltage divider assumes zero “external” load on Vout. Quote: "Resistors only drop voltage if current flows through them and the amount dropped depends on the current"..
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Electrical Load
Definition: The device which takes electrical energy is known as the electric load. In other words, the electrical load is a device that consumes electrical energy in the form of the current and transforms it into other forms like heat, light, work, etc. The electrical load may be resistive, inductive, capacitive or some combination between them. The term load is used in the number of ways.
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