The best weaponry available to Ukraine was shattered against the Russian frontline-they can barely even take a few villages,

Ukraine send like two and a half Leos out to see if a frontal assault would work, and it didn't, so they didn't do it again. The vast majority of western systems are still intact and in any case: If things like MBTs and APVs don't get destroyed you're not using them. Things get shot at in wars and it's no secret that a direct artillery hit will kill any tank.

Meanwhile, though, Ukraine is inflicting heavy attrition on Russian artillery, as well as choppers. Don't let the lines on maps confuse you there's a lot happening that isn't visible there.

what I am saying is that the far-right has disproportionate strength in the Ukrainian army

That would mean that all those people who joined since 2014, 2022 are far-right? Which would mean that the whole of Ukraine is far-right. Which makes no sense when you look at the election results with Svoboda having one seat in the Rada.

then in 2022 because it was the best organised forces in the areas seeing the most intense fighting.

Ukraine built its army from 2014, recruiting ordinary people, training them according to NATO doctrine (giving status and independence to NCOs, mission command, such stuff), with NATO help, we sent like a gazillion of instructors. Many many Nazis left Azov after they were integrated into the National Guard, and the whole thing was actively depoliticised.

Are there still Nazis in Azov? Almost certainly. But the days of them dominating and openly running around with SS runes on their helmets are definitely over. Just as a side note btw Azov is and always was Russian-speaking, Ukrainian nationalism gets complicated.

I do not see how Ukraine can win this-even with western weaponry they have failed in their counteroffensive.

No. Ukrainian generals have been very clear about this from the beginning: The offensive is going to drag on for a very long time due to the lack of materiel to do anything big. Conditions have improved somewhat with Stormshadow and Taurus is bound to come soon but Ukraine has no weapons with which it could just obliterate Russian artillery en masse which would then allow them to bring in slow and vulnerable materiel to clear minefields etc. to enable them to break through the line with heavy armour. They, as already said, have to slowly grind down Russian artillery where they can.

The other way would be actual air superiority. Dunno if those F16s will suffice to switch to full NATO strategy but it's certainly going to give the Russian side quite some trouble.

Speaking of NATO strategy that's probably the reason this impression exists: Yeah if Ukraine had a fully equipped NATO army they'd disable the whole Russian rear from the air, then parachute in armour to attack the Russian lines from the rear and the whole thing would be over in no time. The kind of not war but beating you saw on TV so many times. Like Operation Desert Storm. But Ukraine doesn't have a fully equipped NATO army, it's a Soviet-style army half-way switching to NATO doctrine drip-fed some NATO surplus.

Oh another tidbit: Russia mobilised all its reserves to the front, quite some while ago. Ukraine didn't they're rotating troops in and out. Which is why you see renewed conscription drives in Russia, which then poses the question on what kind of equipment they're supposed to be equipped with, not to speak of the additional instability doing that causes.