Why is a general call for all companies to leave an aggressor state problematic?

Because it amounts to a comprehensive economic embargo, and comprehensive embargoes cause huge humanitarian harm to the civilian population, hitting the weakest and most vulnerable groups hardest.

If every company leaves, the effect is the same as a total economic embargo. Such embargoes can have enormous humanitarian effects on civilians in the target country, and possibly in the companies' home countries too. Weakening an economy reduces the money available for war, but also for the health system; past sanctions have even hit essential goods and medical supplies.

This is the tension at the heart of the paper. Complicity theory, pushed to its conclusion (the tax argument), demands total withdrawal. Just war theory's principle of discrimination forbids deliberately harming civilians. A blanket withdrawal risks doing exactly that.