Retaliating against a foreign country's import tariffs When Trump imposes tariffs on imports from China, he is hurting American consumers who won't be able to take advantage of cheap Chinese goods. If China was to retaliate by imposing tariffs on imports from the US, they would be hurting Chinese consumers in the same way. So, is there is any need for a country to retaliate against another country's import tariffs?
If you're using a simple standard model of trade, like the Ricardian model, trade is good and all tariffs, price floors, price ceilings, etc are bad. Retaliatory tariffs will still be problematic for the country imposing them. I think your reasoning is fine in this regard.

However, trade occurs over many many years. Responding to the initiation of new tariffs by imposing temporary tariffs will reduce the short-term welfare for everyone, including the tariff initiator.  The country which began this "trade war" will then have lower welfare from both sets of tariffs.  Hopefully, the initiating country will remove their tariffs and return to normal.

The retaliating country has some short-run cost, but if it leads to a final low-tariff state, retaliation may be worth it in the long run.

Imagine the game is a repeated version of the following:

\begin{array}
\\ &amp; Free Trade &amp; Tariff 
\\ Free Trade&amp;(5,5)&amp;(3,4)
\\ Tariff &amp; (4,3)&amp;(2,2)
\end{array}

Where for some reason a party has ended on Tariff, perhaps because they have a "trembling hand" with regard to policy.  Note this is different then the prisoner's dilemma because the payoff does not increase as a result of imposing tariffs.