meaning - The difference between は and を?

Hello everyone as the title states I am having difficulty understanding when to use the correct particle.

As an example

肉は食べません (I do not eat meat)

and

やさいを食べます (I eat vegetables)

Is it acceptable to use both wa or o in both these sentences? Wouldn't the first sentence be more correct if I were to say 私は肉を食べません. The reason I chose these two specific sentences is because I saw them in a book. I can not understand why in one sentence they used は while in the other they used を even though they have the same basic structure.

Thank you for any help you may provide!

Answer

[野菜]{やさい}を食べます。 vs 野菜は食べます。

Grammatically speaking, both are correct. They're different in meaning and usage.

を is the object marker. 野菜を食べます is usually an unmarked statement to say "I eat/someone eats vegetables". The は can be, roughly speaking, the topic particle (主題の「は」) or the contrastive particle (対比の「は」). For example, you can use them this way:

「普段、朝食に何を食べますか？」--「野菜を食べます。」(not は)
"What do you usually have for breakfast?" -- "I have vegetables."
「鈴虫は何を食べますか？」--「ナスやキュウリなどの野菜を食べます。」(not は)
"What do bell crickets eat?" -- "They eat vegetables such as aubergine and cucumber."

Here, the を marks new information (新情報).

「普段、野菜は食べますか？」--「はい、野菜はたくさん食べます。」(not を)
"Do you eat vegetables regularly?" -- "Yes, (lit. As for vegetables, I eat a lot. →) I eat a lot of vegetables."

The は is the so-called "topical/thematic は". Here, it marks old/known information (旧情報/既知情報).

は can also be used this way:

「野菜は食べます。でも肉は食べません。」
"I eat vegetables. But I don't eat meat."
「鈴虫は*、肉は食べませんが、野菜は食べます。」
"Bell crickets don't eat meat, but they eat vegetables."
_{*The は in 鈴虫は is a topic marker; there can be only one topical は in a clause. If you see two は's in one clause, at least one of them should be contrastive.}

The は here is the so-called "contrastive は". (You could refer to this thread for more about the contrastive は: What's the difference between wa (は) and ga (が)?)

---

肉は食べません。 vs 肉を食べません。

Again, they're both grammatically correct, and different in meaning and usage.

The は can be topical/thematic:

「お肉はよく召し上がりますか？」--「いいえ、肉はまったく食べません。」(not を)
"Do you eat meat often?" -- "No, I don't eat meat at all."

The contrastive は is also used to mark or highlight the negated element in a sentence:

普段、朝食に肉は食べません。
I usually don't have meat for breakfast (can imply: but I have something else).
普段、朝食には肉を食べません。
I usually don't have meat for breakfast (can imply: but I do for dinner).
普段は、朝食に肉を食べません。
I usually don't have meat for breakfast (can imply: but I do today).

Here, the は shows the scope of negation: 肉を* is negated in the first sentence, and 朝食に is negated in the second, and so on.
_{* When 「XXを」 or 「XXが」 is marked with a は, the は replaces the が or を, as in 「XXは」 rather than 「XXをは」「XXがは」.}
There usually is some negated element in a negative sentence, and therefore you'll more frequently see a は in a negative sentence.

As for the example using an を, you'd use it in a context like this:

「子どもの好き嫌いが激しくて…。」--「何を食べてくれないんですか？」--「野菜をぜんぜん食べないんです。」(not は)
"My child is so picky about food..." -- "What does s/he not eat?" -- "S/he doesn't eat vegetables at all."
_{You'd reply with 「～を」「～が」「～に」「～と」「～から」 etc., not 「～は」「～には」「～とは」「～からは」 etc. to questions 「何を」「何が」「どこに」「誰と」 etc., as in: 「何がないんですか？」「消しゴムがないんです。」(not は) / 「誰と連絡がつかないんですか？」「山田さんと連絡がつかないんです。」(not とは）}