A recent report concerning the new 2,300 foot long bridge between Norway and Sweden told of King Harold V of Norway stating that the new bridge was a strong symbol of the unity between the brother nations.
I have seen the term sister countries or sister cities utilized frequently. Is there any basis for calling 2 nations brother or sister countries or are the terms used arbitrarilly
Just a stab…
But as a matter of poetic perspective…a brotherhood represents the strength of the sentiments, as in fight to the death for one another
Where as a sisterhood reference is meant to draw forth a feeling of emotional solidarity…more heart than braun as it were.
Meaning: Brotherhood = We are going to kick your ass - take names later…and Sisterhood = we, like mother, have unconditional love but we hate guns, can’t we talk it out?
English works with both metaphors but apparently prefers use of the feminine personifications. It’s your mother country, your sister city, etc. I suspect that the exceptions are motivated in large part by something quite similar to MADAME’s suggestion.
However, it’s interesting to note that a large portion of the uses one runs into of someone referencing a “kinship-term political unit,” it is a translation from another national language, as, here, Norwegian. French, German, Russian: all have standard metaphorical uses that tie into the national cultural norms. Die Vaterland means something different than “mother country,” and the difference is not just in the gender of the metaphorical relative.
And with the strong anti-war sentiment of the Scandinavian nations generally, I think that probably “brother nations” is merely a Norse usage literally translated.
Like the German Vaterland, the Norwegian language refers to “Father country” (Fedrelandet). (The word might also be read as “the country of our (fore)fathers”. I’m no linguist, so I don’t know what the origin of the word is.)
Another way to read the “brother country” allegory, is that brothers tend to bicker and fight, and that rivalry between brothers is often fierce. 
I’m not sure it’s so much an anti-war sentiment as a realistic assessment of the might of our armed forces. You don’t have to go very far back in time to find much more aggressive Scandinavian policies. A hundred years ago, Norway and Sweden were on the brink of war. The Swedish king and government chose to give Norway full independence when the Norwegians wanted to get out of the union. If they hadn’t, a war is not unlikely.
<nitpick> Oh, and it’s king Harald V, not Harold. </nitpick>