On its own war is defined as a state of armed conflict between different nations or states or different groups within a nation or state.

A trade war does not include armed aggressions (which typically has life or death consequences) but all of the other aspects of widespread conflict including unpleasant results apply.

Illogical

War, whether violent and destructive with associated loss of life or just destructive making lives miserable rarely have outcomes that are worth the cost.

The trade war results in negative impacts for all participants and even for the innocent bystanders (the global community).  Waging this kind of operation has an emotional foundation but if logic were applied there would never be a war of any kind.

In the television series Star Trek, the fictional Vulcan race was culturally based on pure logic.  As a people, they could not think and act in any way that was not logical.  Hence, no wars, of any type, ever.

Justification

The current US versus China trade war is based on fairness.  The US accused the Chinese of not operating with fairness in the realm of trade.

Fairness defined as impartial and just treatment or behavior without favoritism or discrimination.  Unfortunately, all of these descriptors are very subjective.

What one person, group or another entity view as just or without favoritism could easily be quite different from others perspective.  So ultimately the trade war is justified by a biased opinion leading to emotional angst between all the stakeholders.

We can see how this can lead to war.  How illogical.