I think the idea is that tariffs cut both ways. They increase prices for foreign goods as well as reduce demand for imports causing job losses in the exporting country. The original tariffs increase prices and the retaliatory tariffs reduce demand for American products causing job loss.
> They increase prices for foreign goods
Not only for foreign goods. If there's a tax on imported X, domestic X producers can now charge more because the foreign producers must raise their prices to pay for the tax.
Another way to look at it is that any tariff reduces foreign competition, with all the knock-on effects that implies.
Yes but since Canada is also initiating new tariffs (they've had existing ones for specific products and industries already) so anything said here applies to Canada as well.
For example Canadian tariffs increase prices and their retaliatory tariffs also reduce demand for Canadian products leading to job losses.