watasi ha ryouri ha tokui desu ga, e ha amari tokui de ha arimasen.

Because each は is doing a slightly different job.

• 私 は sets the overall topic: as for me
• 料理 は marks cooking as one item being contrasted
• 絵 は marks drawing/painting/pictures as another contrasted item
• で は in ではありません is part of a fixed grammatical pattern, not a separate topic marker in the same sense

So the sentence structure is roughly:

• As for me, cooking is something I’m good at, but art is not something I’m very good at.

Japanese often uses は to create contrast:

• 料理は得意です = I’m good at cooking
• 絵はあまり得意ではありません = but I’m not very good at art

This kind of repetition is normal in Japanese.

Both are possible, but they feel a little different.

• 私は料理が得意です is a more neutral statement:
  As for me, I’m good at cooking.
• 私は料理は得意です adds contrast:
  As for me, cooking is something I’m good at (implying there may be other things I’m not good at)

In your full sentence, that contrast becomes explicit:

• 料理は得意ですが、絵はあまり得意ではありません。

So using 料理は helps set up the comparison between cooking and art.

得意 and 上手 are similar, but not identical.

• 得意 = something you are good at; a strong point; something you feel confident in
• 上手 = skillful, good at doing something

In many cases, both work:

• 料理が得意です
• 料理が上手です

But there is a nuance difference:

• 得意 often feels more like this is my forte / I’m good at this
• 上手 focuses more directly on skill

Also, 得意 is a na-adjective / adjectival noun, which is why you get:

• 得意です
• 得意ではありません

There could be, but the speaker chose は for contrast.

A very basic pattern is:

• 料理が得意です = I’m good at cooking
• 絵が得意です = I’m good at art

But in this sentence, the speaker is comparing the two:

• 料理は得意ですが、絵はあまり得意ではありません。

Using は highlights the contrast:

• cooking → good at it
• art → not very good at it

So が would sound more neutral, while は is especially natural when comparing categories.

Here, が means but or although.

• 料理は得意です = I’m good at cooking
• 料理は得意ですが、絵は… = I’m good at cooking, but as for art…

This が connects two clauses and introduces contrast.

Important: this is not the subject marker が.
It is a conjunction attached to the polite verb form:

• です + が

A common beginner translation is:

• ..., but ...

あまり usually means not very when used with a negative form.

So:

• あまり得意ではありません = not very good at it

This is a very common pattern:

• あまり好きではありません = I don’t like it very much
• あまり行きません = I don’t go very often
• あまり上手ではありません = not very skillful

By itself, あまり does not usually mean very in modern beginner-style usage.
You normally learn it as:

• あまり + negative

ではありません is the polite negative form used with nouns and na-adjectives like 得意.

Since 得意 is a na-adjective, the negative is:

• 得意ではありません = is not good at / am not good at

A more casual or conversational version is:

• 得意じゃありません

And an even more casual form is:

• 得意じゃないです
• 得意じゃない

So:

• ではありません = formal/polite
• じゃありません = polite but more conversational
• じゃない = casual

All are common, but ではありません sounds the most textbook-polite.

It is separated to show the grammatical pieces more clearly.

In normal writing, you would usually see:

• 得意ではありません

But grammatically, this contains:

• で
• は
• ありません

This breakdown helps learners notice the structure, but in real Japanese text it is typically written together as:

• ではありません

So the spacing is for study purposes, not because native speakers normally write it that way.

It can mean several related things depending on context:

• picture
• drawing
• painting
• sometimes broadly art

In this sentence, 絵はあまり得意ではありません most naturally means something like:

• I’m not very good at drawing/painting
• I’m not very good with art

English translation depends on what sounds natural in context. Japanese often leaves that broader than English would.

Not always. Japanese often omits things that are already understood from context.

So in conversation, someone might simply say:

• 料理は得意ですが、絵はあまり得意ではありません。

That would still naturally mean:

• I’m good at cooking, but I’m not very good at art.

私 is included when the speaker wants to make the subject explicit, or when it helps the sentence sound clearer for learners.

Because it uses polite forms:

• です
• ではありません

This makes the sentence appropriate in neutral or polite conversation.

A casual version would be something like:

• 私は料理は得意だけど、絵はあまり得意じゃない。

So the original sentence is a polite way to say the same idea.