Is there a word or term to describe when someone focuses on a specific example, rather than the problem at large?

For those who don't play video games, there's a growing trend in the industry called "Microtransactions" - a small fee the player can pay for certain things in game. Usually something small, such as a cosmetic item to change the color of their equipment, or a fancy Mount to ride on. Usually, these convey no actual benefit to the player aside from looking cool and unique. But there are games that abuse this (especially on mobile devices) where you can pay for convenience; get experience faster, objectively better items or other advantages, pay now for extra Lives or whatever.

Having defined that term, I had a discussion recently about the trend of Microtransactions and how so long as a game doesn't implement them in a manner that gives paying players an objective advantage over other players I think they're perfectly fine. I cited a game as an example of one that I was told implements these microtransactions unfairly, and I was apparently misinformed.

The other person in the discussion then went on a tangent about how the example game is totally fine and how wrong I was, completely ignoring my initial statement that the discussion is actually about and discrediting everything I said because of a poor example.

Is there a phrase, term, or something to describe the train of thought where a person "pokes holes" in a specific example and overlooks the greater picture like this?

Answer

Argument from fallacy could work. (It's also called argumentum ad logicam or fallacy fallacy, among other things.) Logically Fallacious, a database of logical fallacies, describes it this way:

Description: Concluding that the truth value of an argument is false based on the fact that the argument contains a fallacy.

Logical form: Argument X is fallacious. Therefore, the conclusion or truth claim or argument X is false.

In your case, then, your argument that Example Game used microtransactions unfairly was false, while your conclusion may or may not have been false. However, the other person used this fallacy to claim that because one of your arguments was false, your entire conclusion was false.