This "design" came out of a few different things:
1. I had not looked into private methods in ruby yet.
2. I wanted to write a unit test, but didn't know how to mock away the File io, so I created a method that took two arrays and compared those. 

Looking at it now, I would probably "overload" the compare method like you mentioned in your comment.
Comparator.compare_files(file1, file2)
Comparator.compare_arrays(arr1, arr2)

Looks like ruby does not support method overloading though.(do you have any suggestions or design tricks in light of that fact?)

I hadn't looked into class methods either. The tutorial that I worked through only used instance methods. Continuing to think about the design more (within the context of class methods), I don't think the constructor (initialize method) is necessary. Two class methods would work fine. Do you have any suggestions about how to mock out the file io aspect of this? Is there a way to make a file from a string without saving it to disk, and then using those file objects in the unit test?