Why the dative "ihrem" instead of the nominative "ihrer" or the accusative "ihren"?

Question

In the following sentence, why the dative "ihrem" instead of the nominative "ihrer" or the accusative "ihren"? How do we know that we are supposed to use the dative case here?

Ihrem Vater ging es nicht gut.

Thank you in advance.

Answer 1

The verb phrase is es geht and it already includes the dummy subject es. That phrase is similar to English it works.

Es ging nicht gut. — "It worked not so well."

But in German, you can always add a dative object, which is the one who benefits or has the loss from the action.

Es ging ihrem Vater nicht gut. — "It worked not so well" to her father.

And of course you can make the dative object the topic.

Ihrem Vater ging es nicht gut. — To her father, "it worked not so well."

Answer 2

This is a tricky one.

First off, "(nicht) gut gehen" is an idiom and means "(not) being well (off)" or "(not) doing well". The Substantiv in this sentence is "es" (this is in Nominativ) and "Ihrem Vater" is in fact an Objekt.

Why this Objekt is in Dativ and not in Akkusativ is everybodies guess, maybe an etymologist could answer that. There are rules for which of the object cases (Genitiv, Dativ, Akkusativ) is going into which phrase, but there are at least as many exceptions as there are rule-conforming cases. These rules are more rules of thumb than real rules.

"Geht (es) nicht gut" is a general phrase, how exactly the adressee is not doing well can be specified by an Adverb (or phrase acting like one). Unlike the analogous phrase "(being) well", which, without any specification, is predominantly understood as in regards of health, the german phrase is indifferent about the reasons:

Ihrem Vater ging es gesundheitlich nicht gut.
_{Her father was not doing well in terms of health.}

Ihrem Vater ging es finanziell nicht gut.
_{Her father was not doing well financially.}

Answer 3

Why the dative "ihrem" instead of the nominative "ihrer" or the accusative "ihren"?

Dative verbs are often used to describe what the goal or action of the receiver is, usually a person being addressed (His father was not doing well.)

Ihrem Vater ging es nicht gut.

When encountering these new verbs in sentences, first ask yourself the following (specifically in German):

1. Person: "Ihm geht es nicht gut." (He is not doing well) (Who?/Wem?)
2. You: "-Wem geht es nicht gut?" (Who is not doing well?)
3. Person: "Ihrem Vater geht es nicht gut!" (Her father is not doing well)

Verbs with similar dative declination:

1. Bringen (Bring' mir den Ball.)
2. Anbieten (Sie bietet mir Ratschläge.)
3. Erklären (Ich erkläre dir die Geschichte.)
4. Empfehlen (Ich empfehle ihm ein Restaurant.)
5. Leihen (Leihe mir bitte dein Auto.)
6. Geben (Gib mir das Buch.)
7. Schenken
8. Schreiben
9. Wünschen
10. Schicken
11. Zeigen

More about Gehen being declined into all 4 cases.