Иногда людям трудно извиняться, хотя они понимают свою ошибку.

Because Russian often uses an impersonal construction with words like трудно (difficult, hard).

The pattern is:

кому? + трудно + infinitive
= it is hard for someone to do something

So:

• людям = to people / for people (dative plural)
• трудно = difficult
• извиняться = to apologize

Literally, the sentence starts as:

Sometimes to people it is difficult to apologize.

A more natural English version is:

Sometimes people find it hard to apologize.

In Russian, words like трудно, легко, можно, нельзя, важно often act like short predicative words in impersonal sentences.

So instead of saying something exactly like people are hard, Russian says:

• Мне трудно понять. = It is hard for me to understand.
• Ему легко говорить об этом. = It is easy for him to talk about that.

There is no present-tense to be word here. Russian normally omits is/are in the present tense.

So:

людям трудно извиняться
literally = to people difficult to apologize

Извиняться is the imperfective form, while извиниться is perfective.

Here the sentence is talking about a general situation or repeated fact:

Sometimes people find apologizing difficult.

When Russian talks about something in general, it often prefers the imperfective infinitive.

Compare:

• Трудно извиняться. = Apologizing is hard / It is hard to apologize in general
• Трудно извиниться. = It is hard to apologize once / to manage to apologize

So in this sentence, извиняться fits better because it describes the action in a broad, general sense.

The verb извиняться is the normal Russian verb meaning to apologize.

It is reflexive in form, but you should learn it as a whole vocabulary item:

• извиняться = to apologize
• извиниться = to apologize (perfective)

Russian also has:

• извинять / извинить = to forgive / excuse someone

So the reflexive and non-reflexive forms are different:

• Я извиняюсь. = I apologize.
• Я извиняю его. = I forgive/excuse him.

That is why -ся matters here.

Хотя means although, though, or even though.

It introduces a contrast:

• людям трудно извиняться = people find it hard to apologize
• хотя они понимают свою ошибку = although they understand their mistake

So the idea is:

They know they were wrong, but apologizing is still difficult.

Because хотя introduces a subordinate clause.

Russian punctuation usually separates the main clause from the subordinate clause with a comma:

• Иногда людям трудно извиняться, хотя они понимают свою ошибку.

This is similar to English:

Sometimes people find it hard to apologize, although they understand their mistake.

Russian often uses the reflexive possessive pronoun свой when the possessor is the same as the subject of the clause.

In the clause:

они понимают свою ошибку

the subject is они (they), so their own mistake is expressed with свою.

This is more natural than их ошибку here.

Compare:

• Они понимают свою ошибку. = They understand their own mistake.
• Они понимают их ошибку. = They understand someone else’s mistake / their mistake depending on context, but it sounds less direct for their own.

So свою clearly points back to они.

Both words are in the accusative singular feminine, because they are the direct object of понимают (understand).

Base forms:

• своя = feminine nominative singular
• ошибка = mistake, nominative singular

In the accusative singular feminine:

• своя → свою
• ошибка → ошибку

So:

понимают что?
свою ошибку

Russian often uses the present tense for a general truth or typical situation.

Here the sentence means something like:

Sometimes people find it hard to apologize, although they do understand their mistake.

So понимают is not just about one specific moment. It describes what happens in such situations generally.

Also, after хотя, the present tense is completely normal when talking about a current or general fact.

Yes, often it could.

Literally:

• понимают = understand
• свою ошибку = their mistake

But in natural English, depending on context, this often means:

• they realize they were wrong
• they understand their mistake
• they know they made a mistake

So the Russian phrase is slightly more literal, but the English translation can be adjusted for naturalness.

Иногда means sometimes.

It sets the whole statement as a general observation rather than an absolute truth:

• Иногда людям трудно извиняться... = Sometimes people find it hard to apologize...

Russian word order is flexible, so иногда could move, but placing it at the beginning is very natural.

For example:

• Иногда людям трудно извиняться...
• Людям иногда трудно извиняться...

Both are possible, though the first is the most neutral here.

Not really. This is a natural shift.

The first part uses an impersonal structure:

• людям трудно извиняться = it is hard for people to apologize

Then the second clause switches to a normal personal clause:

• хотя они понимают свою ошибку = although they understand their mistake

So людям and они refer to the same general group, but each clause uses the grammar that fits it best.

This kind of shift is very common in Russian.

Yes. Russian could also say:

Иногда человеку трудно извиняться, хотя он понимает свою ошибку.

That means:

Sometimes a person finds it hard to apologize, although he understands his mistake.

The plural людям is often used for general statements about people as a group, much like English people.

A helpful stress pattern is:

Иногда́ лю́дям тру́дно извиня́ться, хотя́ они́ понима́ют свою́ оши́бку.

A few useful notes:

• Иногда́ — stress on the last syllable
• лю́дям — stress on лю
• тру́дно — stress on тру
• извиня́ться — stress on я
• хотя́ — stress on the last syllable
• понима́ют — stress on ма
• свою́ — stress on the last syllable
• оши́бку — stress on ши

Getting the stress right will make the sentence sound much more natural.