Sigh. They aren't asking you the question because they expect you to write an in-memory data structure library. They are asking you this question because they want to know that you can reason about systems with subtle behavior, and a binary tree is one such system that most programmers learn about in school.
So if you refuse to engage, they'll have no evidence from you about your ability to write subtle code of any kind. And they'll go with someone less snarky who they know does.
