Tariffs have a couple downsides other than the ones most people seem to focus on. One is the impact on exporters. Tariffs increase costs of downstream producers, which makes their exports less competitive vs. foreign competition. The effect this can have is to encourage domestic exporters to offshore their production for export, which means loss of US jobs and hurts our trade deficit.
Another reason economists don't like tariffs is that they enable the domestic producers to be less efficient. Essentially, if you impose a 25% tariff on a commodity that's being imported, domestic producers have little incentive to sell their version for much less than that 25% inflated price. This hurts the viability of their goods on the export market and it means they're in for a rude awakening if/when those tariffs ever get relaxed.