The reason for the tariff war is because he wants more companies to come to United States. So he thinks increasing tariff of each country will help that to happen.
But it is very possible that this will fail. He has paused the tariff for each country for 90 days but he increased China tariff instead.
People will always buy products that are cheap. The cost of production in the US will always make items produced there more expensive than Chinese products. Trump's plan for industries to relocate to the US is not feasible unless Americans will be willing to buy more expensive products.
Bullies don't like being bullied, this is my interpretation of the increase of China's tariff. Trump claims that many countries are "kissing his ass" begging to negotiate. He is angry because China refused to be bullied and decided to stand tall. The 90day pause has brought fresh air to the global economic climate.
Trump also said that this tariff war is to reduce trade deficit. This will not also work. Nations might not also buy expensive US exports, when they can get it cheaper from other countries. This Trump tariff will simply encourage US trading partners to seek other alternatives elsewhere.