why did Hitler only have one testicle?

Because the other, as everyone knows, was in the Albert Hall, his mother having fed it to the fishes when he was small.

Kelley, in Unruly Audience (2020) notes that Colonel Bogey's March (composed in 1914) was “the most frequently heard marching tune in the [British] Army... whistled and hummed everywhere” and had already acrued a vast variety of bawdy 'alternative' lyrics from British soldiers by the end of the First World War, many of which were subsequently passed on to civilian audiences in the interwar period. By the outbreak of the Second World War in 1939, the song was well established in Britain as a long standing parody/comedy vehicle, having also recently undergone something of a pop-cultural revival after being featured in the 1938 Hitchcock film The Lady Vanishes.

The lyrics which found popularity during the Second World War are not particularly remarkable in their bawdiness for the period (a popular alternative version went "Bollocks! And the same to you!") but found rapid popularity for making figures of fun of the Nazi leadership, as well as impugning their manliness and ability to fight. As Kelley notes, the song...

became immensely popular among Allied troops, who in transmitting this song were exercising something of a wartime convention by demeaning the sexual faculties of enemy leaders. But the mockery extended beyond just the Nazis' sexual capacities. Since the 1920s, the words balls or ballsy had come to denote notions of courage, nerve, or fortitude. In that sense, defective testicles rendered the Nazis defective soldiers.

As the lyrics pertain:

Hitler has only got one ball

Goering has two but very small

Himmler has something similar

And Goebbels has no balls at all.

Apart from the obvious internal rhyme of Goebbels and 'no balls', it's noteworthy that Nazi propagandist Josef Goebbels, also ridiculed as the 'poisoned dwarf' in Allied propaganda, is singled out has having 'no balls at all' given both his propagandist role and his position as one of the few senior Nazis to have no history of military service during the First World War. As to the fate of Hitler's other ball, it's in the Albert Hall:

His mother

The dirty bugger

Cut it off when he was small.

For a genuine look at Hitler's actual testicular situation and the trope of ridiculing Hitler (and wider Nazi) sexuality and sexual adequacy, please consult /u/Commiespaceinvader 's excellent post here.