Waluigi is perhaps one of the most interesting characters in the Mario series. It makes sense that Wario would seek out Mario as a rival; Mario’s the most popular hero of the Mushroom Kingdom. But Luigi is the sidekick, the second fiddle, always under Mario’s shadow. So, why would Waluigi choose Luigi as his nemesis?
Not much is known about Waluigi’s past. The first game he appeared in wasn’t even a main Mario game, it was the spinoff Mario Tennis (although to be very specific, an early version of Waluigi appeared as a one-off joke in a Mario manga six years earlier). He appeared in this game basically as Wario’s tennis partner for doubles, and mirrored Luigi in the same way that Wario mirrors Mario. He's lanky with a purple color scheme, as opposed to Wario’s thick build and penchant. It might seem that Waluigi is Wario’s less accomplished brother, shoehorned into copying Luigi’s aesthetic to fit his brother’s theme.
The problem with this theory is that Waluigi may not be Wario’s brother. Although early games referred to Waluigi alternatively as Wario’s “little brother” and “traitor friend,” Charles Martinet, the voice actor for both Wario and Waluigi, explained their relationship as “two nice, evil guys who found each other.” This make Waluigi’s choice in rivalry with Luigi even more confusing. He certainly isn’t Luigi’s evil twin either, but for some reason he decided to become the green plumber’s archenemy. Did he hate Luigi before even meeting Wario? Was their partnership just a happy coincidence?
There might be an answer that satisfies the mystery of Waluigi. Sports seem to be much more dramatic in Mario’s universe. Waluigi can use abilities like creating tornadoes in tennis and growing walls of thorny vines in soccer that can’t be part of regulation play. Maybe Mario sports are more of a form of entertainment, with colorful characters that “compete” each with their own gimmick. In this case, Waluigi is a heel, and his partnership with Wario is part of his gimmick as the villainous foil to fan favorites Mario and Luigi. This fits in perfectly with Nintendo director Shigeru Miyamoto’s confirmation that the Mario cast is actually “a troupe of actors.” Waluigi isn’t actually Luigi’s sworn enemy, he’s just a performer that has to keep up the kayfabe of Mario sports.
Waluigi may be a copy of a sidekick character, but that doesn’t prevent him from being a fan favorite. Whether Waluigi truly hates Luigi as much as he seems to or whether it’s part of his sports persona, we may never know. Like much of the backstory of the lanky purple evil-doer, it may remain a mystery.