Even a country that could produce anything more cheaply than another would economically benefit from foreign trade. Making anything more cheaply is not the same as making everything more cheaply. A country with the ability to produce anything more cheaply has an absolute advantage, but not necessarily a comparative advantage.
Resources are finite, both material and labour. It is wisest to allocate these scarce resources to produce the most profitable goods. With 100 men equally capable of producing steel or computer software, it may be more economically advantageous to develop the software and buy the steel elsewhere. This arrangement is sensible even if the steel is more expensive to buy from elsewhere because the money made producing the software more than accounts for this.
Another analogy may help. A world-class surgeon who is also a masterful hairdresser would better serve his interests and the interests of those around him if he spent his time performing life-saving operations rather than cutting hair.
The beauty of comparative advantage is that it gives even the poorest countries a role in the free market.