Two countries will have zero incentive to trade if their production possibilities curves are parallel straight lines because

One country has a comparative advantage in the production of both goods, thus providing that country with no incentive for trade.

The opportunity costs for both countries are the same.

One country has an absolute advantage in the production of both goods, thus providing that country with no incentive for trade.

An intersection of the two lines is not possible, and therefore trade equilibrium is not possible.