I haven't been familiar with trade wars before Trump. What I don't understand is what there is to win for the EU by suddenly imposing its own tariffs... that will slow down its own economy, even possibly cause social unrest. If US wants to do tariffs, fine, but there is no need to compound on the damage.
The point is to inflict pain on the aggressor; in general no-one ‘wins’ a trade war, and the goal is to make things bad enough for the aggressor that they back down.
In this case, the aggressor inflicted much pain on _itself_, before the tariffs really even went into operation, that it has already partially backed down, but that’s kind of unusual that it would happen so quickly.