Blaine Buxton gives a great example of why "private" methods can be a problem:

I look through the class and find a methood called gatherFiles(File,String,result). It takes a file and determines if it is a test class. Well, a simple check to see if the file is a jar, add the class names of the entries which are tests to the result, and we were in business, right? Well, that's what I thought! So, I overrode gatherFiles, added super to let it do its job, and then, added my jar functionality. Simple right?! It didn't compile. It seems gatherFiles is a private method and I didn't have any visibility for the super. OK, I then just copied the original gatherFiles in place of the super and a little gentle refactoring. Everything compiled, but it worked like the old one. It then struck me. You can't override private methods. GRRRRRR! So, I wound up copying the remaining methods that I needed and removed ClassPathTestCollector as my superclass. It shocked me to know what should have been a simple refactoring, turned into a lot more, and it forced me to commit the worst of all sins: Duplicate code.

The problem with "features" like private and final are that they assume perfect knowledge of all possible future uses of code by the original author. That's simply impossible, and Blaine's found a great example of it.