は vs. が when topic is implied

Question

I was surprised by a conversation listed in my textbook. The conversation goes like this:

A: ハンバーガーを[食]{た}べますか。 
B: いいえ、ハンバーガーは[嫌]{きら}いです

As for the meaning, I believe I understand it. ("Do you eat hamburgers? ... No, I hate them.") However, I interpret line "B" as a shortened version of いいえ、[私]{わたし}はハンバーガーが[嫌]{きら}いです. I think it would be incorrect to say いいえ、ハンバーガーは[私]{わたし}が[嫌]{きら}いです - I interpret this as the jocular "hamburgers don't like me". So what I'm confused about is if the 私は was dropped because the subject was implied, why did the が particle change into は? Is this typical?

Or is my fundamental understanding of the distinction between は and が just off in general (which would not be surprising)?

EDIT: I guess an alternative question would be "would it be wrong for me to say 「いいえ、ハンバーガーが嫌いです。」"

Answer 1

What's important is to grasp what's talked about, that is, the topic.

In this conversation, they are talking over "hamburgers", so (as long as the context goes straightforwardly) you must first think to refer to the hamburgers as the topic, in other words, marked with は. (In this regard, the example sentence saying ハンバーガーを is not really natural. It should be ハンバーガー食べますか？ when you invite the listener to eat it, or ハンバーガーは 食べますか？(or ◯◯さんは ハンバーガー を/は 食べますか？) when you ask about his dietary habit.)

So, replying to the example question as いいえ、ハンバーガーが嫌いだ doesn't work unless it implies a hidden context that questions what the listener hates to eat in the moment among possibly available choices (or it appears in a sub clause like いいえ、ハンバーガーが嫌いなので…).

I don't know what logic enables us to interpret ハンバーガーは… as 私はハンバーガーが, but anyway, when you add 私 to ハンバーガーは食べる, it becomes 私はハンバーガーは食べる (as long as 私 is a shared information).

The structure of Aは Bが… is essentially Aが Bが… with A topicalized. So, when B is topicalized too, it becomes Aは Bは….

Edit: 嫌い doesn't only mean "to hate" but also "I hate", "you hate", "s/he hates", "we hate" or "they hate". So, ハンバーガーは嫌い doesn't so much imply presence of "I" as it's not missing from the beginning. (This interpretation is more reasonable because adding 私は could more or less change nuance of the sentence.)

Answer 2

Your suggestion, ハンバーガーが嫌いです, is a grammatical sentence. Actually the first sentence is the same as this except that ハンバーガー is marked with は instead of が because it's the topic of the sentence. That is what は is for, after all; it marks the topic by replacing が or を. The following is also grammatical:

B: ハンバーガーは食べませんが、ホットドッグは食べます。

Now these は are replacing を.

Where は should appear depends on the context. I said ハンバーガーが嫌いです is not incorrect, but it does sound odd in this context because it lacks the topic even though you're describing some general fact. In most cases, Japanese sentences needs a topic, which can be a grammatical subject or a grammatical object.