The Baby Clothing Tariff

The American Enterprise Institute's James Pethokoukis notices that Canada, as a measure to help young families, has unilaterally eliminated its tariff on imported baby clothes. He suggests that America do the same and eliminate our tariff on imported baby clothes, which is imposed at an overall average rate of 10.8 percent of the price of the goods. Sounds good, but why stop there? Why not eliminate tariffs on all imported clothing, or on imports altogether, rather than picking one group (young families) to favor over others?