Curious item - what on earth's it for?

Any suggestions as to what this is, it’s got my family pretty baffled.
The inside part slides out very easily and there are 2 slots down the side. The wear patterns on the inside part also look pretty curious.
It’s about 1 1.5 inches square.

It looks to me like a cigar cutter. To cut the end off a cigar before smoking. Possible?

That’s the best suggestion I’ve heard so far, but the wear marks don’t really look right to me for that. If it was you’d expect to see some wear in the inside of the insert where they rolled the cigar. Also why would the inside hole be square?