I assume by "right wing" you are actually trying to mean Republicans and their followers. But both Democrats and Republicans are right-wing. Republicans oppose Democrats' wars, sometimes only rhetorically while they materially support them as soon as they get down off the podium, and sometimes (somewhat) materially because they, themselves, would rather be fighting different wars at the moment or making other (e.g. domestic) changes that require them to get the upper hand in the moment in their petty bickering with their donkey-branded co-fascists.

In politically opposing a war for any reasons, you are going to search for arguments that help convince large numbers of people to agree with you and back your political moves. The truth lends powerful such arguments. So Republicans wind up using (some) truth in their arguments against the war that has been the Democrats' baby for the last 15 or so years. Biden was fighting this war back when he was vice president, and Obama let him and Hillary and the other neocons he put in the State Department pretty much have it, while he got off on personally overseeing drone murders in Syria and other places. It's part of a larger NATO expansion and "new" (same as the old) Cold War that both Democrats and Republicans have been waging since the 1980s. But this facet of it has become the Democrats' baby. So (some) Republicans oppose it. Often rhetorically, but some—and growing now, as it's losing its new-car smell—oppose it more materially because they'd rather be focusing on China.

Leftists, on the other hand, oppose this war because being anti-war is necessary and inherent to leftism. So we're going to use some of the same fact-based arguments that people who oppose it for other reasons also use. NATO provoked this war. It orchestrated a coup in Ukraine, and it backed Ukraine's fascist government as it went about the goal of committing genocide against people in Donbass and eastern Ukraine in general (and Jews, and Roma, etc.). And it gleefully threw weapons and Ukrainian lives and Europe's heating and much of Europe's economy into the grinder in an effort to "bleed Russia". There's not really any disputing that if you simply look at the history, and don't delude yourself about imperialism or how things extended back a long way past February 2022. If Republicans touch on some of that, just know that they're not doing it for the right reasons, and they'll gladly twist it into nationalism, antisemitism, anti-Slav bigotry, etc. in a heartbeat. Don't be fooled. Aspects of the truth can be used as propaganda too (at its heart, propaganda isn't just a synonym for "lies", but manipulation based on emotion and other social influence rather than real argument). But because it's not grounded in consistent philosophy or principle, it's only a fleeting affair and will resist attempts to tie it into a broader analysis that would be consistent with the momentary, opportunistic stance. Do Republicans oppose imperialism? Of course not. Do they oppose war? Of course not. Do they oppose genocide? Of course not. Do they want working-class people to have a say in how we wield arms? Of course not.