Short circuit = zero voltage?

If you assume ideal components in a circuit you will get contradictions - you can't have A because B.

An ideal voltage source has no internal resistance and will deliver a constant voltage regardless of current.

An ideal short circuit will have zero resistance, hence must have zero voltage across it regardless of current.

If you connect an ideal short circuit across an ideal voltage source, you have an impossible situation - both a fixed voltage (from the voltage source) and zero voltage (due to the ideal short circuit) between the same two points.

In the Real World, voltage sources do have some internal series resistance (for batteries) or limited current capacity (for power supplies), and any conductor will have some resistance, all of which will limit the maximum current that can flow, and the resulting voltage across the voltage source/short circuit.

No resistance. Finite current. No voltage across. These are the assumptions for an ideal conductor. That makes the short circuit look like an ideal conductor. When doing benign [small signal] circuit analysis, the ideal conductor assumption is useful. When analyzing something less benign that can glow and melt, ideal conductor assumptions might no longer be useful.

Different kinds of assumptions for different kinds of problems.