Few people disagreed with him because almost no one knew he existed during his own time. His impact came later as it became clear that his message was in fact prescient. In fact that became clear when Europe fell into the World Wars and it was clear that Nihilism was the key product of the Western worldview ultimately. Nietzsche following Hegel was an ultra-romantic, i.e. one who saw that rationalism and the enlightenment was ultimately bankrupt because it led to the Terror of the French Revolution, and ultimately to the utter destruction of Europe as a civilization by World Wars and the Cold war aftermath.
The essence of Nietzsche’s thought after Hegel was to incorporate Evolution and to reverse everything possible in prior thinkers. So he reverses Hegel by searching for a way for the Noble to have self-consciousness. He reverses Schopenhauer by attempting to be positive about life and its prospects. He reverses Wagner by rejecting the Christianization of the Pagan mythologies. Of course he then reverses many long held beliefs that were unquestioned within the western worldview such as the necessity to know tow to Christianity as a religious belief system. Or the idea that Germany of his time was represented civilization. Or the idea that colonializaton was the manifest destiny of Europe, and Europe was doing the world a favor by taking control and destroying indigenous worlds and raping and pillaging the entire earth. So basically Nietzsche went after as many Sacred Cows of the European tradition as he could. And of course that did not go over well with those who discovered his work initially. But because his basic position on European Barbarity held true as shown by the fall of Europe into true barbarity of the World Wars people realized that his philosophy was grounded in some reality no matter how unpalatable his attacks were on Sacred Cows, like Christianity. And of course that led to others doing similar questioning of those same Sacred Cows and thus we get 20th century philosophy. Almost every philosopher in the 20th century was profoundly influenced by Nietzsche. This is because Nietzsche saw the rot in the European worldview prior to it falling apart by the mutual self destruction of the European powers. The reason for World War One was that expansion in Europe was based on the colonializaton of the world by the European powers, and when they ran out of territory to suck in to their empires overseas then they fell into Warfare amongst themselves in Europe itself, because the only way to grow was to take over each others territory. But they did not realize that the War in Europe would be so devastating. It was so devastating that it called everything into question, and Nietzsche has already questioned everything prior to the internecine warfare within Europe as the empires collapsed on themselves.
Nietzsche’s own philosophy is a bit incoherent because it is based on the idea of reversing everything that prior philosophers of the generation just prior to him believed. So for instance he attacks Socrates and Plato and adopts the stance that the Pre-socratics were better. Philosophically this is the equivalent of rejecting Christianity as a religion. But Nietzsche struggled to make all these reversals make sense together and developed the idea of the Free Spirit as one who was unfettered in his thinking and could think completely outside the box that had restricted thought up to his time. He wanted to get the coherence he sought in spite of his strategy of rejecting everything, i.e. being an “Academic” from the point of view of Skepticism, i.e. saying No to everything previously thought, yet saying Yes to life, where as previous thought said No to life (so even this is a reversal). He found that possibility of coherence when he discovered the question concerning the Value of Values. He said this was his greatest discovery, because it gave coherence to his strategy of reversal. In effect his reversal of everything thought before was a value in the field of possible values, and we could look at every value in that field and ask what the value of that value was. Nietzsche claimed that reversal of all other values was more valuable than any other value in the field. And that was because it gave freedom from the negative consequences of the other values that were anti-life. Because he came after Darwin Nietzsche could take life and evolution as the basis of all positive values. So that mean that anything that destroyed life, or rendered it non-viable was a poor value. And his position was that all prior values within the tradition were anti-life. This proved itself to be true shortly after the turn of the century when the entire set of European empires fell into destroying each other through mechanized and trench warfare.
So the question after Nietzsche was to what extent a given philosophy affirmed life rather than death.