Du irrst dich, der Kurs beginnt heute, nicht morgen.

Because German normally expresses you are mistaken / you’re wrong with the verb sich irren.

• sich irren = to be mistaken
• Du irrst dich = You’re mistaken / You’re wrong

Du bist falsch is not how German usually says this about a person’s opinion. It sounds unnatural in this context.
falsch is more often used for things like:

• Die Antwort ist falsch. = The answer is wrong.
• Das ist falsch. = That is wrong.

So when talking about a person being mistaken, sich irren is the standard choice.

Because the verb is reflexive: sich irren.

That means it is used with a reflexive pronoun:

• ich irre mich
• du irrst dich
• er irrt sich
• wir irren uns

So dich is not an extra object added for emphasis; it is part of the normal verb pattern.

Because sich irren takes a reflexive pronoun in the accusative, not the dative.

Compare:

• du irrst dich
• ihr irrt euch
• wir irren uns

So:

• dich = accusative
• dir = dative

You simply have to learn sich irren as a verb pattern:
sich + accusative reflexive pronoun

The infinitive is irren, and in this meaning it is usually learned as sich irren.

irrst is the 2nd person singular present tense form:

• ich irre mich
• du irrst dich
• er/sie irrt sich

The -st ending marks du.

German often joins closely related independent clauses with just a comma, especially in natural speech and writing.

So this sentence has two main clauses:

1. Du irrst dich
2. der Kurs beginnt heute, nicht morgen

The second clause explains or corrects the first. In English, you might use a period, dash, or something like You’re mistaken: the course starts today, not tomorrow. German can simply use a comma here.

German usually uses articles more often than English.

So where English may say:

• Course starts today

German more naturally says:

• Der Kurs beginnt heute

Here der is the masculine nominative singular article for Kurs.

This is because der Kurs is the subject of beginnt.

German often uses the present tense to talk about the near future, just like English does.

• Der Kurs beginnt heute.
• The course begins today.
• The course is starting today.

This is completely normal German. You do not need a special future tense here.

German does have a future form, for example:

• Der Kurs wird heute beginnen.

But that sounds less natural in this everyday situation.

Because German main clauses usually follow the V2 rule: the finite verb comes in second position.

In this clause:

• der Kurs = position 1
• beginnt = position 2
• heute = the rest

So the structure is:

• Der Kurs beginnt heute.

This is standard German main-clause word order.

Because nicht usually comes before the specific thing it is negating.

Here, the sentence contrasts two time expressions:

• heute
• morgen

So nicht morgen means not tomorrow, directly correcting that idea:

• Der Kurs beginnt heute, nicht morgen.

It is similar to saying:

• today, not tomorrow

German places nicht right before morgen because morgen is what is being negated.

Not in exactly this structure.

sondern is used after a full negation, usually with nicht or kein, to mean but rather / but instead.

For example:

• Der Kurs beginnt nicht morgen, sondern heute.

That is also correct and very natural.

But in your sentence, the structure is:

• Der Kurs beginnt heute, nicht morgen.

This is a shorter contrast pattern: X, not Y.

So both are correct, but they are built differently:

• heute, nicht morgen
• nicht morgen, sondern heute

Yes. Du is the informal singular you.

So:

• Du irrst dich = informal, used with friends, family, children, classmates, etc.

A formal version would be:

• Sie irren sich, der Kurs beginnt heute, nicht morgen.

Notice two things:

• Sie is capitalized when it means formal you
• the verb changes: Sie irren sich

Yes, startet is also possible.

• Der Kurs beginnt heute.
• Der Kurs startet heute.

Both mean the course starts today.

The slight difference is style:

• beginnen is a bit more neutral and standard
• starten can sound slightly more informal or modern in some contexts

For a course, beginnen is extremely common and very natural.

Du irrst dich can sound direct, especially in conversation. German has softer ways to correct someone.

For example:

• Ich glaube, du irrst dich. Der Kurs beginnt heute, nicht morgen.
  = I think you’re mistaken. The course starts today, not tomorrow.

• Ich glaube, der Kurs beginnt heute, nicht morgen.
  = I think the course starts today, not tomorrow.

So the original sentence is correct, but it is fairly straightforward and explicit.

Yes, morgen can mean:

• tomorrow
• in the morning in some contexts, usually as part of phrases like am Morgen

In this sentence, morgen clearly means tomorrow because it is contrasted with heute:

• heute, nicht morgen = today, not tomorrow

If German wanted to mean in the morning, it would usually be expressed differently, for example:

• am Morgen
• morgens

So there is no real ambiguity here.