When a male unzips his fly and 'whips out' his penis, thus demonstrating how big he is. This can also refer to any situation where a male takes his dick out.
This expression refers to the legendary press conference where, when asked why the U.S. continued to fight the Vietnam war, President Lyndon Johnson "unzipped his fly, drew out his substantial organ, and declared, 'this is why!'"
Any event where males try to prove their worth by comparing their (often irrelevant) possessions/attributes, especially when size is involved. Good examples are the comparisons of engine or salary sizes. This meaning originates from the idea that he whose penis is larger is superior; primitive males would 'waggle their dicks' to show whose was bigger.
Reporter: President Johnson, why are we still fighting the war in Vietnam?
LBJ: (unzips his fly, draws out his substantial organ): This is why!
Onlooker 1: Dude, that guy just whipped it out like LBJ! It's like the whole war is just a big dick waggling contest!
Onlooker 2: That IS LBJ, fool.