Concept:
Volcanic (extrusive igneous) rocks are formed by the rapid cooling of lava at or near the Earth's surface.
Shale, however, is a sedimentary rock formed by the compaction of fine clay and silt particles.
Step 1: Classify the given rocks.
• Obsidian $\rightarrow$ Volcanic igneous rock.
• Pumice $\rightarrow$ Volcanic igneous rock.
• Rhyolite $\rightarrow$ Extrusive igneous rock.
• Shale $\rightarrow$ Sedimentary rock.
Step 2: Identify the rock not of volcanic origin.
Since shale is formed by deposition and compaction of sediments,
\[
\boxed{\text{Shale is not of volcanic origin}.}
\]
Therefore, the correct option is
\[
\boxed{(D)\;\text{Shale}.}
\]