There is a scene in the Monty Python film Life of Brian where the protagonist tries to stop a brawl between two factions of anti-Roman rebels. “Brothers, brothers,” he urges, “we should be fighting together.”
One of the combatants points out, “We are!”
The verb to “to fight” in English can be slippery. With a direct object, it does default to “fighting against”, if the object is a combatant or an enemy — but if it is a conflict itself, you can only guess from context.
Someone who is “fighting the Iraq War”, is he out in the desert, dodging (or setting) IEDs? Or is he marching in a protest, calling for to bring the troops home? No way to know from the sentence itself.
If the object is some cause, condition, or situation, as in the original example, it’s almost always against: if you are fighting suppression, deportation, or cancer, you are fighting against them.
“For” and “against” remove the ambiguity but “with” deepens it. A man fighting “with” his brother might equally well be in some contention with the sibling, or allied with him against a common foe.