How to filter entries by slug in url segment?
I think there is just some confusion between what should be a string or not. From the docs on Parameter Value Syntax:


  To exclude entries with a given value, you must pass in a string, prefixed with not


To that end the following should work for your example:

{% for entry in craft.entries.section('news').slug('not ' ~ craft.request.getSegment(2)).limit(6) %}...