In foro puella non vult a turba premi, sed a matre duci.

Because puella is the subject of vult: the girl does not want...

With verbs like volo (I want), Latin often uses a subject + infinitive construction:

• puella vult duci = the girl wants to be led
• literally, the girl wants to be led

So even though puella is the receiver of the actions in premi and duci, she is still grammatically the subject of the main verb vult.

Because they are present passive infinitives.

• premi comes from premo, premere = press, crush
• duci comes from duco, ducere = lead

Their passive infinitive forms mean:

• premi = to be pressed / crushed
• duci = to be led

So the sentence means that the girl does not want to be pressed by the crowd, but to be led by her mother.

Because volo commonly takes an infinitive to express what someone wants.

Examples:

• vult ire = she wants to go
• vult manere = she wants to stay
• vult duci = she wants to be led

In this sentence:

• non vult ... premi ... duci means
• she does not want to be pressed ... but to be led

This is very normal Latin structure.

Yes. The non goes with vult, and that negation covers the whole contrast:

• non vult a turba premi, sed a matre duci

This means:

• she does not want to be pressed by the crowd, but rather to be led by her mother

So the idea is not:

• she does not want X, and she does want Y stated with two separate verbs,

but rather:

• she does not want X, but instead wants Y

Latin often lets sed handle that contrast without repeating vult.

Because with a passive verb, Latin often uses a/ab + ablative to show the personal agent: the person or group doing the action.

So:

• a turba premi = to be pressed by the crowd
• a matre duci = to be led by [her] mother

This is the regular way to express by someone with the passive.

They are ablative because they follow a, which takes the ablative case here.

Their dictionary forms are:

• turba, turbae = crowd
• mater, matris = mother

In the ablative singular, they become:

• turba
• matre

So:

• a turba = by the crowd
• a matre = by the mother

In foro means in the forum / marketplace.

The preposition in takes the ablative when it means in or on in a location:

• in foro = in the forum
• in urbe = in the city
• in casa = in the house

If in meant motion into something, it would usually take the accusative instead.

So here foro is ablative because it shows place where, not movement.

Sed means but.

It sets up a contrast:

• non vult a turba premi
• sed a matre duci

That is:

• she does not want to be pressed by the crowd
• but [she wants] to be led by her mother

So sed contrasts the two infinitive phrases very neatly: not this, but that.

Because Latin often leaves out a word when it is easily understood from the context.

So this:

• puella non vult a turba premi, sed a matre duci

effectively means:

• puella non vult a turba premi, sed [vult] a matre duci

English can do something similar:

• She does not want to be pushed, but to be led.

You do not have to repeat wants in English either.

In some contexts, a/ab can mean from. But here, because it is used with passive infinitives (premi, duci), the natural meaning is by.

So:

• a turba premi is understood as to be pressed by the crowd not
• to be pressed from the crowd

The passive construction strongly points to agent, not separation.

A helpful breakdown is:

• In foro = in the forum
• puella = the girl
• non vult = does not want
• a turba premi = to be pressed by the crowd
• sed a matre duci = but to be led by her mother

So the core pattern is:

• subject + non vult + infinitive, sed + infinitive

That makes the sentence a good example of:

• a main verb of wanting
• followed by passive infinitives
• with a contrast introduced by sed