If the plural of ‘man’ is ‘men,’ shouldn’t the plural of ‘German’ be ‘Germen’?

What makes these two words so different that 'man' is changed to 'men', but 'German' is changed to 'Germans'?

Solution 1:

German is from the Latin word germani; unlike the similar-looking demonyms Englishman and Frenchman, it is etymologically unrelated to the word man and does not form a plural the same way.

Solution 2:

Words like human and German are not from man and do not contain the (Germanic) morpheme man, as you say. Only the morpheme man is properly pluralised as men. See the list of words in Tchrist's answer for an overview of which words are from man and which aren't. In human and German, we're dealing with the Latin suffix -anus, which means something vague like "having to do with x", shortened to -an in English.

Cf. Republican (same Latin suffix), Qur'an (an Arabic morpheme): we don't say two Republicen were reading their Qur'en.

The true etymology is very important, because folk etymology is not very common in general and hardly ever accepted by the "writing classes". So it does not often become popular enough to displace the original.

Further, there would be little difference in pronunciation between human and humen, because the last syllable is unstressed; folk etymology normally originates in speech, not writing, which means that this plural would be much less useful to speakers. (In women, a trick was performed by having a differently pronounced first syllable to distinguish between woman (/wʊ-/) and women (/wɪ-/), which words would otherwise be pronounced (almost) the same.)

Solution 3:

It’s because they are not, or are not thought of as being, composed of a base noun which the word man has been pasted on to the end of. Without the word man to start with, you won’t get men out of the plural.

Here’s a longer list of such things: