the free trade argument is that tariffs cause goods to become more expensive, which means that people buy fewer things, which causes industries other than the protected industry to suffer and be forced to shed jobs as they get fewer sales. so overall, the number of jobs stays the same, and wages actually decrease because the overall amount of wealth has decreased.  the jobs that protectionism saves are ultimately subsidised by everyone else, its an example of a big and obvious benefit, with many small invisible costs that overall outweigh the benefits.
United Kingdom