Pater dicit iniuriam amicitiae nocere.

Because this sentence uses indirect statement after dicit.

Latin often expresses X says that Y does Z with:

• a main verb of saying/thinking, like dicit
• an accusative subject
• an infinitive

So:

• Pater dicit = Father says
• iniuriam ... nocere = that injustice/wrong harms ...

If this were a direct statement, you might have:

• Iniuria amicitiae nocet = Injustice harms friendship

But after dicit, Latin changes that into indirect statement:

• Pater dicit iniuriam amicitiae nocere

Normally, yes: the subject of a normal finite verb is in the nominative.

But in an indirect statement, the subject of the infinitive goes into the accusative. That is exactly what is happening here.

So in the underlying direct statement:

• Iniuria amicitiae nocet

the subject is nominative iniuria.

But in indirect statement after dicit, it becomes:

• iniuriam ... nocere

So iniuriam is the subject of the infinitive nocere, even though it is accusative.

Because noceo, nocere takes the dative of the person or thing harmed.

So Latin says literally:

• to harm friendship
• friendship is harmed

with amicitiae in the dative.

This is different from English, where we simply say harm friendship with a direct object.

So:

• nocet amicitiae = it harms friendship
• not nocet amicitiam

This is one of the important things to memorize with noceo:

• noceo + dative

Formally, amicitiae could be either:

• dative singular = to/for friendship
• genitive singular = of friendship
• nominative plural in some contexts

But here the verb nocere strongly tells you it must be dative singular, because noceo governs the dative.

So in this sentence, amicitiae means something like:

• to friendship
• more naturally in English, friendship

It breaks down like this:

• Pater = father, nominative subject of dicit
• dicit = says
• iniuriam = accusative subject of the infinitive
• amicitiae = dative with nocere
• nocere = infinitive, to harm

So the structure is:

• Father says [that] injustice/wrong harms friendship

A very literal unpacking would be:

• Father says injustice to-harm friendship

But good English is:

• Father says that injustice harms friendship
• or Father says that wrongdoing harms friendship

Yes.

English usually uses that in this kind of sentence:

• Father says that injustice harms friendship

Latin does not need a separate word for that here. Instead, it uses the accusative + infinitive construction.

So the idea of English that is built into:

• iniuriam ... nocere

rather than expressed by a separate word.

They are:

• pater, patris = father
• dico, dicere, dixi, dictum = say, tell
• iniuria, iniuriae = injustice, wrong, injury, insult
• amicitia, amicitiae = friendship
• noceo, nocere, nocui, nocitum = harm

In the sentence, their forms are:

• Pater = nominative singular
• dicit = 3rd person singular present
• iniuriam = accusative singular
• amicitiae = dative singular
• nocere = present active infinitive

You know from the combination of the construction and the verb.

1. Indirect statement after dicit requires an accusative subject + infinitive.
2. nocere takes a dative for the person or thing harmed.

So:

• iniuriam = accusative subject of nocere
• amicitiae = dative object/complement with nocere

That means:

• iniuriam is what does the harming
• amicitiae is what receives the harm

So the sense is:

• injustice harms friendship not
• friendship harms injustice

Yes, exactly.

That is the direct statement behind the indirect one.

Direct:

• Iniuria amicitiae nocet = Injustice harms friendship

Indirect after dicit:

• Pater dicit iniuriam amicitiae nocere = Father says that injustice harms friendship

This is a very useful pattern to recognize:

• direct statement with a finite verb
• indirect statement with accusative + infinitive

Yes. Latin word order is more flexible than English because the endings show the grammatical roles.

So these would still mean roughly the same thing:

• Pater dicit iniuriam amicitiae nocere
• Pater iniuriam amicitiae nocere dicit
• Iniuriam pater amicitiae nocere dicit

However, word order can change emphasis. The original sentence is a straightforward, neutral arrangement.

For a learner, the safest approach is not to rely only on word order. Instead, identify each word by its form and construction:

• pater = nominative subject
• dicit = main verb
• iniuriam = accusative subject of infinitive
• amicitiae = dative with nocere
• nocere = infinitive in indirect statement

Iniuria has a range of meanings, including:

• injustice
• wrongdoing
• injury
• insult
• wrong

Which English word fits best depends on context. In this sentence, something like these would all be reasonable:

• Father says that injustice harms friendship
• Father says that wrongdoing harms friendship
• Father says that an insult harms friendship

The grammar stays the same whichever nuance you choose.

Latin has no articles, so pater by itself can mean:

• the father
• a father
• simply father

The correct English choice depends on context.

So this sentence could be translated as:

• The father says that injustice harms friendship
• Father says that injustice harms friendship

If this comes from a textbook, Father says ... may be the most natural choice.