Mi abuelo es terco, pero al final admite sus errores cuando ve que otra persona tiene razón.

Because terco is being used here as a personality trait, not a temporary state.

• ser + adjective = something more permanent or characteristic
• estar + adjective = something more temporary or situational

So Mi abuelo es terco means he is a stubborn person by nature.

If you said está terco, it could sound like he is being unusually stubborn at the moment.

Yes, terco is a very good match for stubborn.

It describes someone who resists changing their opinion or behavior, even when others disagree or when evidence suggests otherwise.

Depending on context, it can sound:

• mildly negative: stubborn
• sometimes almost affectionate: hard-headed

In Spain, you may also hear words like cabezota, which is a more informal way to say something similar.

Pero means but, and al final means in the end or eventually.

So pero al final introduces a contrast:

• first idea: my grandfather is stubborn
• contrasting idea: but in the end he admits his mistakes

It suggests that even though he resists at first, he eventually changes his position.

Because admitir can take a direct object.

Here, the direct object is sus errores:

• admite sus errores = he admits his mistakes

You can also use admitir que + clause when what follows is a full statement:

• Admite que se equivocó = He admits that he was wrong

So both are correct, but they use different structures:

• admitir + noun
• admitir que + sentence

In this sentence, it most naturally means his mistakes.

That is because the subject is mi abuelo, so sus is understood to refer to him.

Spanish su/sus can sometimes be ambiguous because it can mean:

• his
• her
• its
• your (formal)
• their

But context usually makes it clear. Here, the logical reading is:

• Mi abuelo ... admite sus errores = my grandfather admits his own mistakes

Because this sentence talks about something that is understood as a real or habitual situation, not an uncertain future event.

• cuando ve que otra persona tiene razón = when he sees that another person is right

This describes what he typically does whenever that situation happens.

Spanish often uses the present indicative after cuando for habitual actions:

• Cuando llega, cenamos.
• Cuando ve que otra persona tiene razón, admite sus errores.

You would use vea if you were talking about a future or hypothetical situation in a different kind of sentence, for example:

• Cuando vea la prueba, lo admitirá.
  = When he sees the evidence, he will admit it.

Because ver here means to realize / to see that, not physically to see a person.

Compare:

• ve a otra persona = he sees another person
  Here a is the personal a, because the direct object is a person.

• ve que otra persona tiene razón = he sees/realizes that another person is right
  Here que introduces a whole clause, so there is no personal a.

So in this sentence, ve is followed by que + clause.

Literally, tener razón means to have reason, but idiomatically it means to be right.

It is one of the most common Spanish expressions.

Examples:

• Tienes razón. = You’re right.
• No tienes razón. = You’re not right.
• Otra persona tiene razón. = Another person is right.

So you should learn tener razón as a set expression.

Both are possible, but they are slightly different in feel.

• otra persona = another person
• alguien = someone

Otra persona emphasizes contrast with mi abuelo:

• my grandfather sees that someone else is right

It highlights the idea that the correct opinion belongs to a different person, not to him.

If you said cuando ve que alguien tiene razón, the meaning would still work, but it would sound a little less specific in that contrast.

Because Spanish often omits subject pronouns when the verb ending already shows who the subject is.

Here:

• admite = he/she admits
• ve = he/she sees

Since the subject mi abuelo has already been stated, Spanish does not need to repeat él.

A more explicit version would be:

• Mi abuelo es terco, pero al final él admite sus errores...

But that sounds less natural unless you want emphasis or contrast.

Because the whole sentence is describing a general truth or repeated behavior in the present.

• Mi abuelo es terco = he is stubborn
• admite sus errores = he admits his mistakes
• cuando ve que otra persona tiene razón = when he sees that another person is right

Spanish uses the present tense here much like English does for habits and general patterns.

It does not mean only one specific moment. It suggests this is what usually happens.

Yes, and it would sound very natural.

Both are possible, but there is a slight nuance:

• admitir sus errores = to admit one’s mistakes
• reconocer sus errores = to acknowledge one’s mistakes

Reconocer can sometimes sound a little more like acknowledging something that is true, while admitir can sound a little more like reluctantly conceding it.

In this sentence, because the grandfather is stubborn, admite works especially well.