Hablar en público sigue siendo un reto para mí.

Because hablar is being used as a noun-like idea: speaking or to speak in a general sense.

In Spanish, the infinitive often works as the subject of a sentence:

• Fumar es malo. = Smoking is bad.
• Viajar solo da miedo. = Travelling alone is scary.
• Hablar en público sigue siendo un reto para mí.

So here, hablar en público is the whole subject: the activity of speaking in public.

Why not the other forms?

• hablo = I speak, so that would change the meaning completely.
• hablando = speaking, but in Spanish the gerund is not normally used as the subject the way it can be in English.

English often says Speaking in public..., but Spanish usually prefers the infinitive: Hablar en público...

En público is a fixed expression meaning in public or publicly.

Spanish often uses certain prepositional expressions without an article, and this is one of them:

• hablar en público
• aparecer en público
• hacer algo en público

It does not mean in the audience. It means being in front of other people, in a public setting.

If you added an article, the meaning would change:

• en el público would suggest something like in the audience / among the public, which is not what this sentence means.

So en público is the natural idiomatic choice here.

Sigue siendo adds the idea of continuing or still.

Compare:

• Es un reto para mí. = It is a challenge for me.
• Sigue siendo un reto para mí. = It is still a challenge for me / It continues to be a challenge for me.

So the sentence suggests that this has been true for some time and remains true now.

This structure is very common in Spanish:

• Sigue siendo difícil. = It is still difficult.
• Sigue siendo importante. = It is still important.
• Sigo pensando lo mismo. = I still think the same.

Because un reto describes what something is, not a temporary location or condition in the usual estar sense.

Spanish generally uses:

• ser for identity, classification, what something is
• estar for states, location, or conditions

Here, hablar en público is being classified as un reto:

• Es un reto.
• Sigue siendo un reto.

You would not normally say está siendo un reto in this context. That sounds much less natural and usually suggests something happening in a more temporary or unfolding way. For a general statement like this, ser is the correct verb.

Not exactly. Reto means challenge, and it usually sounds more neutral or even slightly positive than problem.

A reto is something difficult that requires effort, but it is not necessarily something negative or disastrous.

Compare:

• un reto = a challenge
• un problema = a problem
• una dificultad = a difficulty

So sigue siendo un reto para mí suggests:

• it is hard,
• it takes effort,
• but it is not automatically framed as something bad in itself.

In Spain, reto is very common and natural in this kind of sentence.

Because para mí means for me in the sense of personal perspective or personal experience.

Here, the idea is:

• speaking in public continues to be a challenge for me

So para mí fits naturally.

Compare:

• Es difícil para mí. = It is difficult for me.
• Es importante para mí. = It is important for me.
• Es un reto para mí. = It is a challenge for me.

A mí is usually used in different structures, often with verbs like gustar, interesar, molestar, etc.:

• A mí me gusta hablar en público.
• A mí me da miedo hablar en público.

So in this sentence, para mí is the right choice.

Yes, Spanish allows some flexibility, although the original order is the most neutral and natural.

For example:

• Hablar en público sigue siendo un reto para mí.
• Para mí, hablar en público sigue siendo un reto.

Both are correct.

The difference is emphasis:

• ...un reto para mí is neutral.
• Para mí, ... puts more emphasis on for me personally, perhaps implying that this may not be true for everyone else.

So yes, it can move, but the original version is the most straightforward.

Because mí with an accent is the stressed pronoun meaning me after a preposition:

• para mí
• sin mí
• a mí

Without the accent, mi means my:

• mi libro = my book
• mi casa = my house

So:

• para mí = for me
• para mi libro = for my book

The accent is important because it distinguishes two different words.

Yes, it is completely natural in Spain.

It sounds clear, standard, and idiomatic. A native speaker would have no problem saying it.

That said, there are other natural ways to express a similar idea, for example:

• Hablar en público todavía me resulta difícil.
• Me sigue costando hablar en público.
• Seguir hablando en público es un reto para mí.
  (less likely if you just mean public speaking in general)

A very common alternative is:

• Me sigue costando hablar en público.

This feels a bit more conversational and means something like I still find speaking in public difficult.

But the original sentence is absolutely good Spanish.

Because reto is a countable noun here: a challenge.

Spanish normally uses the indefinite article in this pattern:

• Es un problema.
• Es un reto.
• Es una buena idea.

If you removed the article and said es reto, that would be ungrammatical in standard Spanish.

So un reto is required here.

No. After seguir, if you want to say continue being, Spanish uses:

• seguir + gerund

So:

• sigue siendo = continues being / is still

Not:

• sigue ser ❌

This is the same pattern as:

• Sigue lloviendo. = It is still raining.
• Sigo estudiando. = I keep studying.
• Sigue siendo difícil. = It is still difficult.

So seguir + gerund is the correct structure here, and siendo is the gerund of ser.