economic theory suggests countries benefit from international trade by producing more of those good and services for which they have a comparative advantage (and less of that for which a country does not have a comparative advantage). However, countries rarely specialize completely, why?

even with international trade, countries rarely specialize completely because

A, all goods and services can be traded internationally
B, some countries would lose as a result of free trade
C, consumers in different countries have homogeneous tastes
D, some countries do not have an absolute advantege producing anything
E, production of most goods involves increasing opportunity costs.

A country has a comparative advantage in producing a commodity if the opportunity cost of producing that commodity in terms of other commodity is lesser than the other country. Therefore, a nation specialize in the production of that good but not fully specialized because of increasing opportunity cost.

If a country has constant opportunity cost then that country would be fully specialized in the production of some good.

Increasing opportunity cost:

Suppose a country produces milk and wheat. It was seen that plane area is suitable for the production of wheat and hilly area is suitable for the production of milk. But suppose a country wants to increase the production of milk. So, there is a transfer of resources from the production of wheat to milk. This transfer going on to increase the production of milk.

But there is a decrease in the productivity of the resources because some of the transferred resources are best suitable for the production of wheat rather than milk.

So, there is a increase in the opportunity cost of producing milk with increase in the output of the milk.