I see what caused the bug. You're supposed to:
Go to the building from my pictures. "No one's there, check the school." Objective updates. To go school. Rescue hostage. Kill the tanks.
What I actually did the first time, was go to the school and rescue the hostage accidentally, when I was clearing the village of threats on my way to the objective. After that it triggered the tank objective, but then the progression halted. Going to that other building first appears to be necessary to complete the level. Keep that in mind if you're playing this mission...