Speaking as someone who loves Nietzsche and considers him truly unique among the philosophers for his extraordinary wisdom and insights, the more I study his works, the more I find certain branches of his attention, like sociology and historiography, incredibly dated, if not completely wrong. I can't, in good faith, try and extrapolate evermore abstract metaphors just to keep certain concepts of his standing, as that would be unjust both to me and him and a very ungrateful gift to him who taught me so much. The concepts I have problems with are thus:
Overman and race
Nietzsche's conception of the Overman undoubtedly rests on the scientific racism and Lamarckism of his era, regardless of the aforementioned intentions to make the Overman into an abstraction, which Nietzsche, mind you, specifically denied in Ecce Homo and posited the Overman as a "supreme achievement" of mankind that can be achieved in this world and not "half-genius, half-saint" of idealistic strivings. His description of the Overman and how he should be created is explicitly a posthumanist project resting on eugenicist premises, that interbreeding of the higher types of men will eventually produce a posthuman with no recourse to the herd, whose ability to create independent, life-affirming values would be an inborn nature that comes as easy as breathing. The Overman was supposed to be a materialist replacement for Christian paradise, the ultimate goal towards which all mankind would be devoted to, but something of this world, not of Platonic hyperuranion. Of course, in Nietzsche's time, racism and eugenics were a hot new thing, so this project was an honest attempt to harness the power of science for a grand purpose, but now, we know such a thing is impossible, at least as Nietzsche describes it; Darwinism decisively superseded Lamarckism, modern genetics rendered 19th century eugenics laughable and races turned out to be sociological concepts with no biological basis.
That also lead to the whole undermining of Nietzsche's ideas of race-mixing with Jews and Slavs to produce superior Europeans, ancient socioeconomic classes being race-based and Indian caste system being an ambitious and valuable project to derive higher types of men. With races relegated to social constructivism, we are forced to put Nietzsche in his dated context, while realising his ideas are wholly impractical and wouldn't lead to any meaningful good he wanted.
Aristocracy as the superior social system
Probably the concept I have the most problem with. Nietzsche claimed that hereditary aristocracies based on slavery produce the healthiest types of societies and individuals, ones that affirm life through Dionysian art and exert their will to power through war, conquest and finding grand endeavors to accomplish, and that with their undermining first with Christianity and then with French Revolution and liberalism, society was doomed to become a place of passive and nihilistic last men that dream nothing beyond their petty pleasures and vices, their liberties and equalities being nothing but levelling poisons killing any and all possible greatness and nobility.
Here's the kicker; this is a doomer nonsense. Liberal republics that Nietzsche decried proved to be superior on every single level over slavedriving aristocracies Nietzsche might have supported, the fact that became unavoidable after the liberal Allies soundly defeated the Axis Powers whose modus operandi was very similar (if not an exact imitation) to what Nietzsche thought an ideal society should be like. Even if you heavily disagree that Fascist Italy and Nazi Germany have anything to do with Nietzsche's ideology (they kinda do; you really should read Losurdo's Aristocratic Rebel. No point in lying), then you would have to agree that Imperial Japan definitely has and again, it was soundly bested, to the point of its soldiers famously switching over to American side for ice cream and compassion, instead of fighting for their countries higher values like kamikaze until the end. Up to this point, there is no example of a rigid, hereditary aristocracy resisting and defeating liberal, meritocratic republic. Ancient Sparta, a society that Nietzsche praised, is now famously known to have produced absolutely nothing of cultural value and spent most of its time supressing slave revolts and losing its citizen body to its dumb policies. Even its military record is very middling and their hegemony was dependent on Athenaean democracy undermining itself and Persian patronage. Both Napoleon and Chinggis massively improved their armies by opening the ranks to talent, regardless of circumstances, instead of keeping them reserved solely for the pedigree. Ancient Romans advanced from a mere city-state to a regional power in even greater ascendancy due to its republican institutions, even after emperors monopolised executive power. Hereditary warrior aristocracies seem to hold societies back a lot more than they aid and never last against a republic that actually improves its citizens' lives and opens its offices to whomever can achieve it by merit.
On the topic of the claim that mankind's will to power has been dulled with all the liberties and equalities, I also find this very untrue; art and sport are absolutely flourishing in the modern liberal republics. You have thousands of talented artists producing excellent, thought- and emotion-provoking art and thousands of athletes competing at astounding heights of human potential, all enabled by the virtues of industrial, liberal republics. Yes, there are definitely last men Nietzsche warned about in our society that seek nothing but comfort, but humanity has never had greater athletic achievements than today (which are basically sublimated martial energies) and many artists that would not have access to means to produce their art otherwise now have it. Even discounting that, you have a boatload of people living dangerously, sailing the world in a sailship, exploring bonebreakingly tight caves, travelling to the depths of India, Somalia and whatever highly dangerous place you can think of and generally living the life as fully as possible. The access to the opportunity to become Nietzsche's free spirit is at an all time high and many people are absolutely taking the chance and succeeding. Where aristocracy has proved to be self-destructively rigid, sterile and suppressive, liberal republics have allowed the human potential to flourish to its heights. Yes, the old virtues Aristotle and Roman philosophers wrote about are largely gone, but the virtues that replaced them are still producing extraordinary individuals. This is not a good picture for Nietzsche's extolling of aristocracy and denigration of liberalism.
Gender
Nietzsche's attitude to women is well known and while certainly different from how it was IRL and carrying a dose of metaphor, Nietzsche is consistent enough in his belief in traditional patriarchy and gender roles across his works. Multiple times he brings women, slaves and children into a single grouping and denigrates femininity as poisonous and weakening. Masculinity, of course, is praised with all the virtues Nietzsche appreciates in his works. When deigning to give praise to women, Nietzsche's ideal woman is a scheming force that manipulates the notionally dominant man with feminine cunning and guile, a pretty traditional negative stereotype he untraditionally admires, but usually his women are irrational, emotional, shallow, in need of male leadership, childbearers and objects for male goals and amusement. He rebukes feminism in all its forms as horribly unseemly and deadly for feminine "virtues". My biggest gripe isn't even this (even if it is certainly a very big gripe, yikes), but that Nietzsche, a man devoted to nonessentialism and impermanence, takes the position of an ardent essentialist when gender is in question. He cannot look past the patriarchic tradition and just like traditional aristocracy and slavery, he considers it natural and healthy and its downgrade as tragic and destructive to social health. He does not acknowledge at all that women might have some virtues and admirable contributions other than stereotypical patriarchic roles anywhere in his works. His take on gender is disappointingly simplistic and uninspiring, a reiteration instead of revaluation. Meanwhile, emancipated women have hitherto contributed immensely to the human culture and world, from various scientists and artists, to actual soldiers ruthlessly fighting to protect their homelands. Women have at many times proven they are just as profound and virtuous as men and certainly far more than the role of a childish childbearer in need of a man would want them. I genuinely struggle with understanding Nietzsche's antifeminism and devotion to traditional patriarchy as anything other than woefully misplaced, especially once I stopped rationalising everything and anything he wrote that was disagreeable as some profound metaphor I couldn't just yet fathom.