Det ene ærme på min skjorte er for langt, men det andet ærme passer godt.

This is a very common Danish pattern:

• det ene ... det andet ... = the one ... the other ...

It is especially used when there are exactly two things in a pair, like:

• sleeves
• shoes
• hands
• eyes

So here, the sentence is talking about the two sleeves of the shirt:

• det ene ærme = one sleeve
• det andet ærme = the other sleeve

Using ene and andet makes it clear that there are two sleeves, and we are comparing them.

Because ærme is a neuter noun in Danish:

• et ærme = a sleeve

Neuter nouns take det in this kind of structure, not den.

Compare:

• det ene ærme because ærme is neuter
• den ene sko because sko is common gender

So the gender of the noun controls whether you use den or det.

Because after determiners like det ene, det andet, min, denne, and similar words, Danish usually uses the noun in its indefinite form, not the definite form.

So:

• det ene ærme
• det andet ærme
• min skjorte

not:

• det ene ærmet
• det andet ærmet
• min skjorten

This is normal Danish grammar. Even though English might suggest the one sleeve, Danish still uses the bare noun form here.

Because lang has to agree with the noun it describes.

Since ærme is a neuter noun (et ærme), the adjective takes -t in the singular:

• et langt ærme
• ærmet er langt

So:

• for langt = too long

If the noun were common gender, you would normally get lang instead:

• en lang kjole
• kjolen er for lang

No. In this sentence, for means too.

So:

• for langt = too long

This is a very important Danish use of for:

• for dyr = too expensive
• for stor = too big
• for svært = too difficult

So although it looks like English for, here it functions like English too.

For the same reason as det: it agrees with the gender of ærme, which is neuter.

So:

• et ærme
• det andet ærme

But with a common-gender noun, you would use anden:

• den anden sko
• den anden jakke

So:

• anden = common gender
• andet = neuter

In Danish, på is very commonly used when talking about parts of clothing or something located on an object.

So:

• ærmet på min skjorte = the sleeve on my shirt

This is a natural Danish way to say it. English often prefers of in similar situations, but Danish commonly uses på.

You will see this pattern a lot:

• knappen på min jakke = the button on my jacket
• lommen på bukserne = the pocket on the trousers

So this is normal idiomatic Danish, not something you should translate word-for-word from English.

Because skjorte is a common-gender noun, not a neuter noun.

• en skjorte = a shirt

So the correct possessive is:

• min skjorte

Compare:

• min skjorte because skjorte is en
• mit ærme would be possible only if you were using ærme with a possessive, because ærme is et

Examples:

• min bog = my book
• mit hus = my house

So the possessive has to match the noun’s gender.

It comes from the verb at passe, which can mean to fit, to suit, or to be the right size depending on context.

Here:

• det andet ærme passer godt = the other sleeve fits well

This is a very useful verb for clothing:

• Skjorten passer godt. = The shirt fits well.
• Skoene passer ikke. = The shoes do not fit.

So passer is the present tense form.

You can say just passer, but passer godt sounds more natural and complete here.

• passer = fits
• passer godt = fits well

The adverb godt adds the idea that the fit is good or comfortable, not just technically possible.

This is very common in Danish:

• Det passer godt.
• Den sidder godt.
• Det ser godt ud.

So godt is not required in every sentence, but it is very natural here.

Yes, Danish could sometimes omit the noun if the meaning is clear from context:

• Det ene ærme er for langt, men det andet passer godt.

That is possible.

But repeating ærme makes the sentence clearer and slightly more explicit:

• det andet ærme passer godt

This is very normal Danish style. Repeating the noun is often preferred when comparing two things, especially in learner-friendly or careful speech.

After men, Danish still uses main clause word order.

So the structure is:

• det andet ærme = subject
• passer = verb
• godt = adverb

That gives:

• Det andet ærme passer godt.

This is important because men does not create subordinate clause word order.

Compare:

• ..., men det andet ærme passer godt.
• ..., fordi det andet ærme passer godt.

Both have passer early, but in Danish it is useful to remember that men introduces another main clause.

Because det ene ... det andet ... is the natural way to talk about one of two and the other one.

That is different from numbering things in order.

• det ene / det andet = one / the other
• det første / det andet = the first / the second

With a pair like sleeves, det ene ... det andet ... is usually the better choice, because the point is contrast within a pair, not counting them in sequence.

So here Danish is saying, in effect:

• one sleeve is too long, but the other sleeve fits well

not:

• the first sleeve ... the second sleeve

Yes, many English speakers find it tricky.

The main things to notice are:

• æ is not an English sound exactly; it is somewhat like the vowel in cat, but not identical
• r affects the vowel quality in Danish
• the final -e is a weak unstressed sound

A rough learner-friendly approximation is something like:

• AIR-muh or EH-r-muh

But that is only approximate. The real Danish pronunciation is more compressed and smoother.

The most important thing is to recognize it as:

• et ærme
• ærmet
• ærmer

If you can hear and produce the æ reasonably well, that is already a good start.