Focusing your attention on certain aspects of the argument while completely ignoring or missing other parts.  This usually results in irrelevant rebuttals, strawman fallacy, and unnecessarily drawn-out arguments.

Logical Form

Information is presented.

Response addresses only some of the information, completely ignoring the rest.

Example A

News Reporter:  The Dow Jones was up 100 points today, NASDAQ closed up 160 points, unemployment is and has been declining steadily, but foreclosures have not budged.

Gary: “Did you hear that?  Our economy is in the crapper!”

Explanation: While there are many problems with the reasoning of Gary, due to his selective attention, and possible pessimism bias when it comes to the economy, he did not let the good news register and/or did not take that information into consideration before concluding that our economy is still in the “crapper”, based on that one piece of news on foreclosures.

Example B 

Most of us are guilty of selective attention when the information is about us.  We tend to embrace the information that makes us feel good and ignore the information that does not.

Exception: Ignoring irrelevant information is a good thing when evaluating arguments.  The key is to know what is irrelevant.

Other Fact: Selective attention is mostly a cognitive bias in that it happens subconsciously. It becomes a fallacy when it shows up in argumentation.