Мой сын боится идти к стоматологу.

Because мой has to agree with сын.

• сын is a masculine singular noun.
• So the possessive pronoun must also be masculine singular nominative: мой.

Compare:

• мой сын = my son
• моя дочь = my daughter
• моё письмо = my letter

Because сын is the subject of the sentence, so it is in the nominative case.

The sentence is about what the son is doing/feeling, and the verb боится agrees with him:

• сын боится = the son is afraid

If сын were functioning differently in the sentence, it might change case, but here nominative is correct.

Боится is the 3rd person singular form of the verb бояться.

So:

• я боюсь = I am afraid
• ты боишься = you are afraid
• он / она / мой сын боится = he / she / my son is afraid

It is singular because сын is singular.

The -ся is the reflexive marker, and it is part of the verb бояться.

In modern Russian, you usually just learn бояться as a whole dictionary verb meaning to be afraid. Even though -ся often has a reflexive origin, with this verb it is best to think of it as simply part of the normal verb form.

So:

• dictionary form: бояться
• sentence form: боится

Because Russian often uses verb + infinitive when talking about being afraid, wanting, being able, needing, and so on.

Here, боится идти means that the son is afraid to do the action of going.

This is very similar to English patterns like:

• afraid to go
• wants to go
• can go

So the infinitive идти is exactly what you would expect after боится when the sentence says what action he fears doing.

This is a very common question.

• идти usually means to go on one particular trip / in one direction
• ходить usually means to go habitually / generally / back and forth

So:

• боится идти к стоматологу = he is afraid to go to the dentist (for this visit / this act of going)
• боится ходить к стоматологу = he is afraid of going to the dentist in general / he is afraid to go there as a regular type of action

In this sentence, идти is natural because it refers to the specific act of going.

Yes, but it changes the nuance.

• идти focuses on the process or act of going
• пойти often emphasizes starting off or taking the step

So:

• боится идти к стоматологу = afraid to go
• боится пойти к стоматологу = afraid to actually make himself go / take that step

Both can be possible in context, but идти is the more neutral choice here.

Because Russian uses к + dative when the movement is toward a person.

A dentist is a person, so:

• идти к стоматологу = to go to the dentist

This is different from going into a place/building, where Russian often uses в:

• идти в клинику = to go to the clinic

So к is not random here; it is the normal preposition for going to a person.

Because after к, the noun must be in the dative case.

The dictionary form is:

• стоматолог = dentist

But with к it becomes:

• к стоматологу

For many masculine singular nouns, the dative ending is -у or -ю.

So:

• к врачу
• к учителю
• к стоматологу

Because Russian has no articles.

English says:

• to the dentist
• to a dentist

Russian usually just says:

• к стоматологу

Whether it means the dentist or a dentist is understood from context. Russian learners coming from English often look for an article, but there simply is not one.

That is an important difference.

• Мой сын боится идти к стоматологу = he is afraid to go to the dentist
• Мой сын боится стоматолога = he is afraid of the dentist

In the original sentence, the fear is about the action of going.
In боится стоматолога, the fear is directed at the person.

So adding идти к changes the structure and the meaning.

The given order is the most neutral and natural:

• Мой сын боится идти к стоматологу.

Russian word order is flexible, but changing it usually changes the emphasis, not the core meaning.

For example:

• К стоматологу мой сын боится идти.
  This puts extra emphasis on to the dentist.

So the original sentence is the best neutral version for everyday use.