The simple reason is that Mussolini came first. He came to power in his famous March on Rome and subsequently became a bit of a role model for nationalist would-be dictators. When Hitler and Ludendorff tried to take power in Munich before a subsequent "March on Berlin" a little more than a year later, the parallels (beyond Blackshirts and Brownshirts) were already so obvious that comparisons between Mussolini and Hitler became quite common within Germany. E.g. von Lossows impression from 1924 that
He thought of himself as the German Mussolini, the German Gambetta, and his followers, who had taken on the inheritance of the byzantinism of monarchy, called him the German Messias
Er hielt sich für den deutschen Mussolini, den deutschen Gambetta, und seine Gefolgschaft, die das Erbe des Byzantinismus der Monarchie angetreten hatte, bezeichnete ihn als den deutschen Messias.
(quoted in Joachim Fest, Hitler, 2003 Berlin, p.292. But note that a contemporary newspaper has the quote without a mention of Mussolini on p. 2)
In fact, the comparisons were common enough to already back then attract objections from certain circles. E.g.
The German National Socialists are most often compared with the Italian Fascists, by friends and foes alike. Which is quite unjust. Fascism is morally and politically no better than German reactionaries, but its fundaments and development are completely different.
Die deutschen Nationalsozialisten werden von Freunden und Feinden meist mit den italienischen Fascisten verglichen. Ganz mit Unrecht. Der Fascismus ist moralisch und politisch nicht mehr wert als die deutsche Reaktion, aber in seinen Grundlagen und
seiner Entwicklung ist er völlig verschieden von ihr.
(Weltbühne 2. Halbjahr 1924, p. 413)
For this reason it is ridiculous to talk about German fascism. An essential difference between Italian fascism and German secret society-ism is that Fascism has positive ideas, while Hitlerism has no ideas, that Fascism has constructive and Hitlerism destructive consequences.
(The term used for Hitlerism here is actually rather derogatory, but I have no idea how to properly translate it.)
Darum ist es
auch lächerlich, von deutschen Fascisten zu reden. Der italienische Fascismus und die deutsche Geheimbündelei unterscheiden sich wesentlich dadurch, daß der Fascismus positive Ideen hat, während die Hitlerei ideenlos ist, daß der Fascismus konstruktiv, die Hitlerei destruktiv wirkt.
(Letter to the editors of Weltbühne from September(!) 1923. Weltbühne 2. Halbjahr 1923, p.252)
For a more complete picture, the National Socialists were not the only German organisation of the 1920s to be called fascist, other violent rightwing organisations were labeled similarly, e.g. in this article from early 1923.
This answer is a bit Germany-centric. For usage in English, I think the ultimative answer is again a mixture of "obvious parallels" and "Mussolini came first". Orwell's 1944 text in which he acknowledges that the term Fascist is applied to Germany a lot has already been mentioned. There is an earlier essay by Churchill from 1937 named "The infernal twins", where one twin is communism and the other one is fascism and national socialism. I am sure there are earlier examples.