Why sinking Lusitania was a strategic mistake

How should the sinking of RMS Lusitania be understood as a strategic decision?

The sinking was a German strategic mistake rather than a British trap: any questionable cargo was outweighed by the damage the attack did to American opinion.

The idea that Lusitania was deliberately offered as a British trap is rejected here. The liner may have carried items in a legal grey area, while British officials probably assumed Germany would not take the political risk. Even a tempting target could not compensate for the effect on American opinion. The decision sits alongside the Zimmermann Telegram as evidence of disordered German foreign policy after Bismarck.