Mater dicit bonam vitam ex divitiis non nasci, sed ex constantia et liberalitate.

Because after dicit Latin commonly uses an indirect statement construction: accusative + infinitive.

So in:

Mater dicit bonam vitam ... non nasci

the phrase bonam vitam is the subject of the infinitive nasci, but in Latin that subject goes into the accusative.

In English we translate it as: Mother says that a good life is not born...

So even though a good life is the logical subject in English, Latin puts it in the accusative because of the indirect statement.

For the same reason: it is part of the indirect statement after dicit.

Latin often says:

• dicit + accusative subject + infinitive

So:

• Mater dicit = Mother says
• bonam vitam ... nasci = that a good life is born / arises ...

If Latin used nascitur, that would be a normal finite clause, not the standard accusative-and-infinitive construction.

Because nasci is a deponent verb.

A deponent verb:

• has passive forms
• but an active meaning

So nasci looks like a passive infinitive, but it means to be born, to arise, or to come into being.

That is perfectly normal for this verb. Its dictionary form is nascor, nasci.

Literally, nasci means to be born. But in this sentence it is being used more figuratively.

So bonam vitam ex divitiis non nasci means something like:

• a good life is not born from riches
• a good life does not arise from wealth
• a good life does not come from riches

Latin often uses a vivid metaphor like being born from to express coming from or having its source in.

Because bonam agrees with vitam.

Vitam is:

• feminine
• singular
• accusative

So the adjective must match it:

• bona vita = nominative
• bonam vitam = accusative

Since the whole phrase is the accusative subject of the infinitive in indirect statement, both words are accusative.

Because they depend on the preposition ex, which takes the ablative case.

So:

• ex divitiis = from riches
• ex constantia = from constancy
• ex liberalitate = from generosity

Here ex expresses source or origin: what something comes from.

Because divitiae is one of those Latin nouns that is normally used only in the plural when it means riches or wealth.

So:

• divitiae = riches
• divitiis = from riches

By contrast:

• constantia = constancy, firmness
• liberalitas = generosity

These are abstract nouns usually used in the singular here.

Because Latin, like English, often omits a repeated preposition when the same one clearly applies to both words.

So:

ex constantia et liberalitate

means:

• from constancy and generosity

with ex understood for both nouns.

Latin could repeat it, but it usually does not need to:

• ex constantia et ex liberalitate

would be more repetitive.

Sed means but.

It sets up a contrast:

• non ... ex divitiis = not from riches
• sed ex constantia et liberalitate = but from constancy and generosity

So the sentence is built as a clear opposition: not X, but Y.

Because Latin word order is much more flexible than English word order. The endings show the grammatical relationships, so Latin does not rely as heavily on position.

This sentence is arranged in a natural Latin way:

• Mater = subject
• dicit = main verb
• bonam vitam ... nasci = indirect statement
• ex divitiis non ... sed ex constantia et liberalitate = the contrast in source

Latin often places important or contrasting ideas where they stand out. Here the sentence emphasizes:

• bonam vitam
• then the contrast between ex divitiis non and sed ex constantia et liberalitate

A good breakdown is:

• Mater — nominative singular, the subject: mother
• dicit — present active: says
• bonam vitam — accusative singular, the subject of the infinitive in indirect statement: a good life
• ex divitiis — prepositional phrase: from riches
• non nasci — infinitive phrase: not to be born / not to arise
• sed — but
• ex constantia et liberalitate — from constancy and generosity

So the structure is:

Mother says [that a good life is not born from riches, but from constancy and generosity].