Seriously, the teachers hear a bunch of exagerated rumors targetting a specific student, and their reasoning is "the rumors must be true!" and not "someone is targetting this kid specifically with the most effective tool available to teenagers"? Is this their first time being teachers? The really stupid thing, and what makes the threat believable to some degree, is that he actually does have eroge in the school. Like seriously dude? You brought enough games to school that you can't fit them into your backpack and smuggle them back out? Because sure, the teachers could listen to the rumors about explosives and do an inspection not expecting to find anything, just to quell the rumors, and end up finding the games instead. But that could have happened at any other point too, so why risk having the games there?
The other question is, why would he be the only one risking expulsion? Wouldn't the entire club be punished if contraband is found in their clubroom? Like, all this rumors going about what happens in the clubroom, shouldn't the rest of the members of the club also be implicated? But because the rumors are about him, apparently everyone else is ignored?