The correct answer is: A. To sidetrack the issue.
To split hairs is to focus on minor details or irrelevant points in an argument, in order to avoid or distract from the main issue. It is a form of logical fallacy known as “arguing from irrelevance.”
Option B is incorrect because quarreling over trifles is to argue about unimportant matters. This is not the same as splitting hairs, which is to focus on minor details in an argument.
Option C is incorrect because indulging in over-refined arguments is to engage in arguments that are excessively complex or technical. This is not the same as splitting hairs, which is to focus on minor details in an argument.
Option D is incorrect because finding faults with others is to criticize others for their mistakes or shortcomings. This is not the same as splitting hairs, which is to focus on minor details in an argument.