The logic is perfectly simple, obscured only by 150 years of obfuscation.
Large companies can do without any one worker. If they negotiate with one worker at a time, they hold all the cards, and have no motivation to listen, only to dictate. But they can't do without a labor force. If their workers come to them with one united front, then management has to negotiate on an equal footing.
Management has seen this reality, and has done everything legal and illegal to squelch labor organizations. Peaceful protests have been broken up with police horses and nightsticks, the Haymarket massacre of 1886. Workers were locked into a burning building, the Triangle Factory in 1911. Labor leader Eugene Debs was jailed for holding strikes that were inconvenient for the employer. Joe Hill was murdered for writing songs that were too effective for inspiring collective action. (Listen!) Lately, the whole idea that labor should be free to organize is tainted with innuendos about foreign influence and associations with communism and Stalin's atrocities.
Since Ronald Reagan, labor unions have lost influence in America, and America -- all of us, workers and capitalists and teachers and artists -- all of us are suffering because the middle class is collapsing. They're still at it, with militarized police forces, and the full and illegal use of FBI agents paid to to subverting movements for social justice. The collapse of Occupy a few years ago was cynically engineered by the Obama Administration.
Organized labor was once the soul of the Democratic Party, which has now slipped comfortably into the pocket of Wall St.
Organized labor means so much more than union rules and higher wages. It means living in a society where ordinary people have freedom and dignity. Without organized labor, democracy may not survive. International Workers of the World, unite!