Он признался, что был неправ.

Because признаться and признать are related but not identical.

• признать usually means to recognize, to acknowledge, or to declare/accept officially
• признаться means to admit or to confess

In this sentence, the idea is that he admitted something about himself, so Russian uses признался.

Compare:

• Он признал ошибку. = He acknowledged the mistake.
• Он признался, что ошибся. = He admitted that he had made a mistake.

So признался is the natural choice here.

The -ся ending is a very common Russian verb ending. It often makes a verb reflexive, but its function is broader than the English idea of himself/herself.

With признаться, it forms a separate verb meaning to admit/confess.

So:

• признать = to recognize / acknowledge
• признаться = to confess / admit

In this sentence, -ся is just part of the normal dictionary form признаться. You should learn it as a whole verb, not as признать + himself.

Because the sentence describes a completed action in the past: he admitted something.

Russian past tense is formed differently from English. Here:

• признаться → признался = he admitted

The ending -л marks past tense, and -ся remains part of the verb.

Also, Russian past tense agrees with gender and number:

• он признался = he admitted
• она призналась = she admitted
• они признались = they admitted

Because что introduces a subordinate clause.

The sentence has two parts:

• Он признался = He admitted
• что был неправ = that he was wrong

In Russian, a subordinate clause introduced by что is normally separated by a comma.

So the comma here is standard and necessary.

Here что means that.

It introduces the content of what he admitted:

• Он признался, что... = He admitted that...

This is very common in Russian:

• Я знаю, что он дома. = I know that he is home.
• Она сказала, что устала. = She said that she was tired.

So in this sentence, что connects the main clause to the statement being admitted.

Both are possible, but they are not exactly the same.

• Он неправ. = He is wrong.
• Он был неправ. = He was wrong.

The verb быть is normally omitted in the present tense in Russian, but it appears in the past and future.

So:

• present: Он неправ.
• past: Он был неправ.
• future: Он будет неправ.

Here the sentence refers to the past, so был is required.

Yes. неправ is the short-form adjective meaning wrong.

It comes from неправый, but in modern Russian this short form is much more common in sentences like this:

• Я неправ. = I am wrong.
• Ты неправ. = You are wrong.
• Она неправа. = She is wrong.

It changes for gender and number:

• неправ — masculine
• неправа — feminine
• неправо — neuter
• неправы — plural

Since он is masculine singular, the form is неправ.

Because неправ means wrong in the sense of not correct / mistaken, especially about a person’s judgment, opinion, or behavior.

неправильный usually means incorrect, wrong, or improper for things such as:

• неправильный ответ = an incorrect answer
• неправильное произношение = incorrect pronunciation

But for a person being wrong, Russian usually says:

• Он неправ. = He is wrong.

So неправ is the natural choice here.

Yes, often it could.

Russian frequently drops subject pronouns when the subject is clear from context. So:

• Признался, что был неправ.

can also work if it is already obvious who is being talked about.

However, он may be included for clarity, contrast, or emphasis. In an isolated example sentence, it is very normal to keep он.

In the Russian past tense, the verb agrees in gender and number with the subject.

Since the subject is он, masculine singular, the past tense form is был.

Compare:

• Он был неправ. = He was wrong.
• Она была неправа. = She was wrong.
• Оно было неправо. = It was wrong.
• Они были неправы. = They were wrong.

So both был and неправ match the masculine subject он.

Yes, you can, but the nuance is a little different.

• Он признался, что был неправ. = He admitted/confessed that he was wrong.
• Он признал, что был неправ. = He acknowledged/admitted that he was wrong.

Both are possible.
But признался often sounds a bit more personal, like he openly admitted it, perhaps after resisting or hiding it.
признал can sound a little more neutral or formal: he acknowledged the fact.

So the original sentence is very natural, especially when the idea is he finally admitted it.

Sometimes you may see both, but in a sentence like this, неправ is the standard and most natural spelling.

• Он был неправ. = He was wrong.

Writing it separately, не прав, is more likely when the negation is being strongly emphasized or contrasted:

• Он не прав, а просто упрям. = He is not right, just stubborn.

For learners, the safest choice in this kind of sentence is to use неправ as one word.