Here's an idealized example. Imagine a state with 1,000,000 people. 400,000 Democrats live in a narrow strip on the Eastern border, uniformly distributed in that strip. The 600,000 Republicans are uniformly distributed in the rest of the state.
Split the population in half by a north-south line. The Eastern district has 400,000 Democrats and 100,000 Republicans, and so has a Democratic representative. The Western district has 500,000 Republicans and so had a Republican representative.
Now try an east-west line. Each district has 200,000 Democrats and 300,000 Republicans. There are two Republican representatives.
Yet on a map, both divisions look fine.
That's one reason the anti-gerrymandering rules specify looking deeper than just population and compactness.
Sometimes you get different outcomes if you divide state in half north-south vs. east-west, depending on how the cluster is divided between districts.