Why is it der Arzttermin?

Arzttermin is a compound noun, and German compounds take the article of their last word: der Termin. So it’s der Arzttermin.

Sense 1
der

Meaning

[1] Date of a doctor

[1] Termin bei einem Mediziner

Examples

On Thursday, Johannes missed his doctor's appointment because of a traffic jam

[1] Am Donnerstag verpasste Johannes wegen eines Verkehrsstaus seinen Arzttermin.

Declension

1 Singular Plural
Nominativ der Arzttermin die Arzttermine
Genitiv des Arzttermines des Arzttermins der Arzttermine
Dativ dem Arzttermin dem Arzttermine den Arztterminen
Akkusativ den Arzttermin die Arzttermine

Pronunciation

Dictionary entries include material from Wiktionary. Wiktionary