Canada too- our dairy products are cheaper and arguably better quality than US and Canadian dairy products.
Producer lobbys in many countries everywhere have huge sway over their governments.
With our new FTA with India I understand there was huge resistance on dairy too because again we are simply more efficient producer than India but India have a powerful farmer lobby group.
But yeah it makes a mockery of US claims to be free trade advocate when US lobbys can so consistently block free trade with long time friendly nations like New Zealand.
A growing number of US traditional allies are now actively forming stronger trade groupings like the TPP as US goes increasingly protectionist...it is imo a lose lose outcome but one that US has chosen.