Learn Hardcore Croatian: Učiteljica kaže da nema smisla raditi usporedbe, jer svatko uči svojom brzinom i ima svoju nadu. - The teacher says that it makes no sense to make comparisons, because everyone learns at their own speed and has their own hope.

the feminine form of “teacher” (male: učitelj, female: učiteljica)
in the nominative singular case, because it is the subject of the sentence.

So the sentence is explicitly talking about a female teacher.
If it were a male teacher, you would say: Učitelj kaže da…

What does kaže da mean as a structure? Why is da used, and why is the verb after it just in the normal present tense?

Kaže da… literally means “(she) says that…”.

kaže = “(she) says”
da = the conjunction “that” introducing a subordinate clause
nema after it is in the ordinary present tense, not a special “subjunctive” form.

Croatian does not have a separate subjunctive like some other languages. After da you usually just use a normal finite verb (present, future, etc.), depending on meaning:

Učiteljica kaže da nema smisla…
“The teacher says that it doesn’t make sense…”
Učitelj kaže da će doći sutra.
“The teacher says that he will come tomorrow.”

Why is it nema smisla and not something like ne ima smisao?

Two things are happening here:

nema vs ne ima
- The negative of imati (“to have”) is almost always used in the contracted form nema, not ne ima.
- On ima vremena. – “He has time.”
- On nema vremena. – “He doesn’t have time.”
smisla (genitive) vs smisao (nominative)
- The basic form is smisao (“sense, meaning”).
- After ima / nema it very often goes to genitive: smisla.
- Set phrase: ima smisla / nema smisla = “it makes sense / it doesn’t make sense”.

So nema smisla is an idiomatic, set expression that literally means “does not have sense” → “it doesn’t make sense.”

Why is smisla in the genitive case after nema?

In Croatian, imati / nemati can take genitive instead of accusative, especially in:

negation (with nema), and
many fixed expressions.

Common patterns:

Ima vremena. / Nema vremena.
“There is time / There is no time.”
Ima nade. / Nema nade.
“There is hope / There is no hope.”
Ima smisla. / Nema smisla.
“It makes sense / It doesn’t make sense.”

So nema smisla uses genitive to express the lack or absence of something in a fairly idiomatic way.
You will also see ima smisla with genitive, not ima smisao in this meaning of “to make sense.”

Why do we say raditi usporedbe? Could we also just use a verb like uspoređivati?

Raditi usporedbe literally means “to make (do) comparisons”.

raditi – “to do, to make”
usporedbe – “comparisons” (accusative plural of usporedba)

This is a very common and natural way to express “to make comparisons” in Croatian.

You can also use the verb uspoređivati (“to compare”):

Nema smisla raditi usporedbe.
“It doesn’t make sense to make comparisons.”
Nema smisla uspoređivati se s drugima.
“It doesn’t make sense to compare oneself with others.”

Both are correct; raditi usporedbe is a noun phrase with a light verb, while uspoređivati is the straightforward verb “to compare.”

What words exactly correspond to “everyone” in the sentence, and what kind of word is svatko?

The word that corresponds to “everyone” is svatko.

svatko is an indefinite pronoun meaning “everyone, everybody.”
It is grammatically singular, so the verb is also singular: svatko uči (“everyone learns”).

Don’t confuse:

svatko – pronoun: “everyone”
svaki – adjective: “every, each” (needs a noun: svaki čovjek, “every person”)

Examples:

Svatko uči svojom brzinom. – “Everyone learns at their own speed.”
Svaki učenik uči svojom brzinom. – “Each student learns at their own speed.”

What case is svojom brzinom, and what does this case express in this phrase?

Svojom brzinom is in the instrumental singular:

svojom – instrumental feminine singular of svoj
brzinom – instrumental singular of brzina (“speed”)

The instrumental is used here in an adverbial way to express manner / way:

učiti svojom brzinom ≈ “to learn at one’s own speed/pace”

So the structure [verb] + (svojom) + [noun in instrumental] often corresponds to “to do something in/at/by one’s own X”:

raditi svojim tempom – “to work at one’s own pace”
živjeti svojim stilom – “to live in one’s own style”

Why is it svojom brzinom and svoju nadu, not njegovom/njenom brzinom or njegovu/njezinu nadu?

This is because of the special possessive adjective svoj, which is reflexive.

svoj means “one’s own” and is used whenever the possessor is the subject of the sentence (for 1st, 2nd, and 3rd person):

svatko uči svojom brzinom
“everyone learns at their own speed”
svatko ima svoju nadu
“everyone has their own hope”

If you used njegov / njezin, it would usually refer to some other person’s speed or hope, not the subject’s own.

Forms here:

svojom – instrumental feminine singular (with brzinom)
svoju – accusative feminine singular (with nadu)

So svoj agrees in gender, number, and case with the possessed noun, just like moj / tvoj / njegov etc., but it always refers back to the subject’s own.

Why is it brzinom and nadu? What are the base forms of these words?

Base forms (dictionary forms) are:

brzina – “speed” (nominative singular)
nada – “hope” (nominative singular)

In the sentence:

svojom brzinom – instrumental singular of brzina
- nominative: brzina
- instrumental: brzinom (ending -om)
svoju nadu – accusative singular of nada
- nominative: nada
- accusative: nadu (feminine nouns in -a typically take -u in the accusative singular when they are animate/in certain patterns)

The verb imati (“to have”) takes the accusative:

ima svoju nadu – “(he/she) has his/her own hope.”

The instrumental brzinom expresses manner (“at (that) speed”), and the accusative nadu is the direct object of ima.

Why is there a comma before jer? Could we also start a sentence with Jer?

Jer is a subordinating conjunction meaning “because”. In Croatian:

A clause introduced by jer is a subordinate clause explaining the reason.
It is normally separated by a comma from the main clause.

So:

…nema smisla raditi usporedbe, jer svatko uči…

You can technically start a sentence with Jer, but stylistically it usually continues what was said before:

Ne trebamo raditi usporedbe. Jer svatko uči svojom brzinom…

In more formal writing, you’d more often connect it with a comma (as in the original sentence) rather than begin a new sentence with Jer.

Can the word order change in this sentence? For example, could we say Svatko svojom brzinom uči i svoju nadu ima?

Yes. Croatian word order is relatively flexible, and your example is grammatically correct:

Svatko uči svojom brzinom i ima svoju nadu.
(neutral, very natural)
Svatko svojom brzinom uči i svoju nadu ima.
(more marked, with extra emphasis on “at their own speed” and “their own hope”)

Changing word order usually changes emphasis or style, not the core meaning.
However, the original order is the most neutral and typical for everyday speech and writing.