In the famous Asian tale of Romance of Three Kingdoms, the warlord Cao Cao controlled most of China, but he was never really able to defeat Liu Bei, a minor warlord who started with nothing. Liu Bei's only claim was he had a (very, very distant) lineage to the Imperial Line, but Liu Bei basically did everything Cao Cao didn't (Cao Cao was domineering and strict, and Liu Bei did the opposite - whatever Cao did, Bei did the opposite) and although Bei never really became stronger than Cao , they are considered rivals to this day.
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Hannibal vs. Scipio and Napoleon vs. Wellington are topics which are still being talked to this day.
The various KPop rivalries which got the attention of the people of the world also deserve to be remembered as such.
I have argued for years that in the end, history will record that IU, not EXO, BlackPInk, Ed Sheeran, The Weeknd or Adele, was BTS' greatest rival.
BTS
Conquered the world
Eventually switched to English lyrics
7 Korean men - a group
Emphasized dance and performance
Had a distinct worldview (although later weakened)
Sold millions of albums
Not the owner of their company, having to answer to Mr. Bang
IU
Remained in Korea
Did not give up using Korean lyrics
1 Korean woman -a soloist
Did not emphasize dance and performance
Did not have distinct worldview (although later began to develop it).
Sold around 150,000 albums until the last one
Was the owner of her company at the height of her fight against BTS, answering only to herself
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Rivals are formed because they are polar opposites. BlackPink falls short as BTS' rivals because BlackPink did not fight BTS during the latter's height, no matter what reason is offered.
IU did fight BTS during the latter's height, and actually succeeded wresting Korea from it, BTS' first loss since its loss to IU's Autumn morning in Sep 2017. I have said a few times that if the giants of pop around the world gave her some more support the whole situation might have been overturned.
One might argue that Vo Nguyen Giap is not a rival of William Westmoreland because Giap did not march his PAVN (North Vietnamese Army) across the Pennsylvania avenue in Washington D.C. But Giap's aim was to remove Americans from South Vietnam, not to conquer USA.
So, although IU's reputation mostly remained in Korea and she did not make a significant inroads into the pop of other countries and mostly remained somewhat influential only in Asia, because BTS could never really conquer IU she does qualify as BTS' greatest rival as the one act it could not subdue.