Extend or Expand

Question

"However, Robertson is no sentimentalist. After devoting years of his life to bears, he is under no illusion about their feelings for him. It is clear that their interest in him does not extend beyond the food he brings."

Why cannot "expand" be used here?

Answer 1

Instead of conceptual extension or expansion, let's first talk about physical extension or expansion, starting with the example in Ricky's answer.

Saying that a forest extends beyond the lakes is a description of how far you can go and still be in the existing forest - you can go beyond the lakes and still be in the forest even if the forest never increases in size. This is an idiomatic use of the word extend - it applies due to the context.

Extend intransitive verb
2 : to reach in scope or application - M-W

Saying that a forest expands beyond the lakes is a description of the forest growing in a particular direction. At first, the land beyond the lakes isn't covered by the forest. Then new trees near the forest germinate and grow, and the forest gets bigger until it covers land that is beyond the lakes. This is a simple use of the word expand.

Expand : to increase in size, range, or amount : to become bigger - M-W

Taking this back to your conceptual extension or expansion, Robertson is talking about the bears' existing interests, so the use of extend is appropriate. If, as Charl E hypothesises, the bears develop an interest in another person, their interest has grown beyond what it was before (there is an increase in its coverage), so we can then say that their interest has expanded.

Answer 2

When something extends (as opposed to when something is extended), no action is required:

The forest extends beyond the lakes.

Expanding something does require some action. It's taking something in hand and enlarging it. The forest expanding beyond the lakes doesn't make any sense.