I think this is the key difference. Conventional wars, regardless of the weapons, are awful, but they take time, and resources, and constant decision making. Things can change, one side withdraws or surrenders and the killing stops.

A weaponised virus doesn't have these constraints, and could destroy humanity, but at least it takes some time, and can probably be somewhat mitigated.

In nuclear war, a split second decision could annihilate every living human, erase all evidence of our existence, and maybe cause a big enough climate shift to permanently end life on this planet.