First on what I mean by linear element and linear circuit.
A linear element has a voltage that is proportional to it's current. A resistor's voltage is proportional to it's current and in the frequency domain capacitors and inductors are also linear elements. This element has a property of superposition such that the output of an input is equivalent to the sum of the outputs of two smaller inputs that sum to the original input.
A linear circuit has a different definition. It is defined by satisfying the superposition theorem, different than the property of superposition mentioned above for the linear element. The theorem states that the voltage or current anywhere on the circuit due to multiple input sources is the same as the sum of the responses which would occur if only one source was turned on at a time. This is very different from the meaning of a linear element whose superposition property only applied to inputs at one location instead of multiple inputs in different locations.
Which brings to my question: Why does a circuit of linear elements create a linear circuit?
Note: The current answers say that linear elements imply a linear circuit without explaining why. Or at least not clearly enough for me to understand.