זאת הסיבה שאני לא יכולה לבוא.

Because in present-tense Hebrew, sentences like X is Y often have no explicit verb.

So:

• זאת הסיבה = This is the reason
• literally: This the-reason

Hebrew usually leaves out is/are in the present tense.
If you wanted past or future, you would use a form of להיות (to be).

For example:

• זאת הסיבה = This is the reason
• זאת הייתה הסיבה = This was the reason
• זאת תהיה הסיבה = This will be the reason

זאת means this and is the feminine singular form.

It matches הסיבה (the reason), because סיבה is a feminine noun.

So:

• זאת הסיבה = This is the reason

If the noun were masculine, you would use זה instead.

For example:

• זה הספר = This is the book
• זאת הסיבה = This is the reason

You may also see זו הסיבה. In modern Hebrew, זאת הסיבה and זו הסיבה are both common.

Because the sentence means the reason, not just a reason.

• סיבה = a reason
• הסיבה = the reason

Here the speaker is identifying a specific reason:

• זאת הסיבה... = This is the reason...

So the ה־ is the definite article, like the in English.

שאני is made of two parts:

• ש־ = that / which / because depending on context
• אני = I

So here:

• שאני לא יכולה לבוא = that I can’t come

In this sentence, ש־ introduces the clause explaining the reason.

A very literal breakdown is:

• זאת הסיבה = This is the reason
• שאני לא יכולה לבוא = that I can’t come

In natural English, we often drop that, but in Hebrew ש־ is very normal here.

Because the speaker is female.

In the present tense, יכול / יכולה means can / able to, and it agrees with the gender and number of the subject.

So:

• אני לא יכולה לבוא = said by a woman
• אני לא יכול לבוא = said by a man

Even though אני means I for both men and women, the word יכול/יכולה shows the speaker’s gender in the present tense.

Other forms:

• הוא יכול = he can
• היא יכולה = she can
• אנחנו יכולים = we can (mixed or masculine)
• אנחנו יכולות = we can (all feminine)

Hebrew usually does not leave the subject out as freely as some other languages do, especially in sentences like this.

Also, יכולה shows:

• gender: feminine
• number: singular

but it does not clearly show person by itself. It could go with I, you, or she, depending on context.

So אני is needed to make it clear:

• אני לא יכולה = I can’t
• היא לא יכולה = she can’t
• את לא יכולה = you can’t (to a woman)

That is why אני is important here.

Because לא negates the idea of being able to.

So:

• אני לא יכולה לבוא = I cannot come / I’m not able to come

The negative word comes before the main predicate:

• לא יכולה = cannot

This is different from putting the negative idea on coming itself.

Compare:

• אני לא יכולה לבוא = I can’t come
• אני יכולה לא לבוא = I can choose not to come / I’m able not to come

That second sentence has a very different meaning.
So in your sentence, לא is in exactly the right place for can’t come.

לבוא is the infinitive to come.

In Hebrew, the infinitive usually begins with ל־, which often corresponds to English to:

• לבוא = to come
• ללכת = to go
• לעשות = to do / to make

So:

• יכולה לבוא = can come
• literally: able to come

The verb בוא (come) is a very common verb, and לבוא is its infinitive form.

Close, but not exactly in structure.

In Hebrew, יכול / יכולה literally means able or capable, but in everyday language it is the normal way to express can in the present tense.

So:

• אני יכולה לבוא = I can come
• literally closer to: I am able to come

English uses a modal verb (can), but Hebrew uses a word that behaves more like an adjective or participle in the present tense and agrees in gender and number.

So the translation is natural, even if the grammar works a little differently.

Yes. That is also correct and very common.

Both of these are natural:

• זאת הסיבה שאני לא יכולה לבוא
• זו הסיבה שאני לא יכולה לבוא

They both mean the same thing: This is the reason I can’t come.

A learner should mainly recognize that:

• זו and זאת can both mean this for feminine singular
• both are used in modern Hebrew

Yes, there are other natural ways to express the same idea.

For example:

• הסיבה שאני לא יכולה לבוא היא... = The reason I can’t come is...
• אני לא יכולה לבוא, וזאת הסיבה. = I can’t come, and this is the reason.
• זאת הסיבה לכך שאני לא יכולה לבוא. = This is the reason that I can’t come.

But the original sentence:

• זאת הסיבה שאני לא יכולה לבוא.

is very natural and straightforward.

A simple pronunciation guide is:

zot ha-sibá she-aní lo yecholá la-vo

A few notes:

• זאת = zot
• הסיבה = ha-si-BA
• שאני = she-a-NI
• לא = lo
• יכולה = yekho-LA or yekho-LA
• לבוא = la-VO

The stress is usually near the end in:

• הסיבה
• אני
• יכולה
• לבוא

So if you say it smoothly:

zot ha-sibá she-aní lo yecholá la-vó

that will sound quite natural.