Considerations when designing a web service from scratch

I have been asked in interviews that if I was to design an API, like a web service, what things would I need to consider. I usually talk about the number of users, whether I'd use Soap or Rest. If it was connected to a DB. I usually mention that'd I'd wire it in with Spring Dependency injection and Spring transactions. The interviewer usually looks at me blankly.

What are the considerations?