One team ends up a player (or two) down, and that’s when a lot fo the scoring happens. Ergo, you fight and you are more likely to lose.

FWIW, this is also why I’m not a hockey fan…

I think you have a misconception about the rules. Hopefully if I clear this up, you may give hockey another shot.

One team ends up a player (or two) down, and that’s when a lot fo the scoring happens

True. In hockey this is called a power play. It's a well known fact about hockey that most of the scoring in a game happens during the power play. Power plays are a common occurrence in every game as a result of standard penalties (ie not fighting) such as high sticking (hitting a player above the shoulders with your stick), hooking (using your stick to 'hook' a player to try and slow them down), slashing (using your stick to whack someone, usually across the hands), etc.

Ergo, you fight and you are more likely to lose.

False. When players fight, they are given equal concurrent penalties. Both of their teams remain at even strength and there is no power play.