Why does French use the definite article in "Mes frères aiment le chocolat" when English omits it?

When a predicate applies generally to a whole class, use the definite article.

Les lions rugissent. Lions roar.

This doesn't strictly mean there are no exceptions. There may be lions that don't roar and types of chocolate your brothers don't like. But when it's intended to be generally true, we use the definite article.

This also applies to abstract nouns.

L'argent ne fait pas le bonheur. Money can't buy happiness [lit. "Money does not create happiness"].

Note that the rule is not reversible. The use of the definite article does not guarantee that you intend to talk about the whole set or that you're talking about an abstract noun. Your brothers might like the chocolate (that has been given to them). The lions (in the zoo exhibit) might roar. The money (you earn) might not create happiness. Here, as my translations suggest, it corresponds to cases where English also uses the definite article.

(Why English is article-free for the other meaning is beyond the scope of this site.)

For a beginner:

English doesn't "drop" the article. There is not one there to begin with in general cases. The general sense (meaning) of your French sentence corresponds to the general sense of the English with no article. Other examples:

• I love apples.
• J'aime les pommes.
• Cats are cute.
• Les chats sont mignons.
• Money makes the world go round.
• L'argent fait tourner le monde.

This is true of all Romance languages (French, Spanish, Portuguese, Italian and Roumanian. In the latter the definite article comes at the end of the word.)

Here is a French teaching site that explains this for beginning learners: alpha-b.fr This is just a fact about French. It is just the way it is.

"Why does French require the definite article « le » in this sentence, while English drops the article when speaking about something in general?"

An actual reason, as for so many things of a similar nature in the study of languages, is not to be known too precisely: sometime in the remote past, someone had the idea that such nouns could be "signalled" by adding an article; what can be said is that the choice of article did not clash in a flagrantly illogical manner with certain principles (it was a definite article not the article "un", for instance) and that it was inspired by the related ideas behind the use of the definite article, the role of which had in the ancient tongue was that of determination.

Latin, from which French originates, had no articles. In the ancient French language, the definite article had a meaning close to that of a demonstrative, and was used when it was necessary to show that a word was a noun; it was not used when there could be no doubt as to the grammatical nature of the word. (From Le Bon Usage 2008, § 585)

In fact, in ancient French (ancien français, "AF" in the text below) the definite article was not used as it is today in modern French, and in particular, it was not used for mass nouns;

L'article défini en ancien français : l'expression de la subjectivité Richard Epstein Langue française Année 1995

En général, un SN muni d'un article défini en AF désigne un être ou un objet concret bien délimité. Si ces propriétés font défaut à un référent, aucun article n'apparaît : « Le nom commun est employé sans article quand il est pris dans sa valeur la plus générale et qu'aucune particularisation n'est requise » (Moignet 1973 : 106-107) :
(3) Hom ki traïst altre, nen est dreiz qu'il s'en vant. [Rol. v. 3974]
Il es juste que [tout] homme qui trahit son semblable ne puisse s'en vanter⁴.

4. Nous mettons entre crochets les éléments que les traducteurs ont insérés dans la version en français mais qui n'ont pas d'équivalents formels dans le texte original.

D'une manière analogue, « les termes signifiant des matières sont employés sans article quand il s'agit de signifier une quantité indéterminée » (Moignet 1973 : 107) :
(4) Mirre e timonie firent alumer [Rol. v. 2958]
Ils font brûler [de la] myrrhe et [de l'] encens

Les noms en question dans (4), mirre et timonie, se réfèrent à des masses dont les identités ne sont pas spécifiées. Comme prévu, ils ne prennent pas d'article.

SN : "syntagme nominal", corresponds to "noun phrase" in English grammar

This shows that the difference between French and English is merely one of choice; whereas both languages initially had the simplest and most natural choice, at some point French departed from it and an article began to be grammatically associated with the word. It is also understandable from this that English does not "drop" the article, since it was not initially associated grammatically with words.

"Please explain the grammatical rule that governs the use of definite articles with general or mass nouns after verbs of preference (like aimer, adorer), and give a few short examples and relevant exceptions."

There is no grammatical rule as concerns this use; you use the proper definite article when the intended idea is the generic one, as below.

• Elle aime le chocolat. Tous adorent l'air marin.
• Elle aime les pâtes.

What can be said is that a partitive idea is not usually combined with these verbs because it does not make sense to do that. As those verbs express a discrimination and as there is the idea of an indiscriminate part in a partitive, some nonsense results. This goes for English. French does not confer any sense to utterances of the type "J'aime du chocolat"; nor does English to "I like some chocolate" (/səm/, a little); in "I'd like some chocolate", which is correct, "like" is not the plain verb "to like" but a verb used to make a polite request. Although "J'aime du chocolat" could have been conceived (not too logically) as meaning "there is a sort of chocolate I like" this is not so (aime du chocolat, aimait du chocolat,a aimé du chocolat.

Addition: comments on edit 1 (version 2) and modifications; thanks to user Segorian for the review

1. An actual reason: I prefer this choice of article in this case because more than one reason, all more or less plausible, might be found. https://books.google.com/ngrams/graph?content=an+actual+reason%2Cthe+actual+reason&year_start=1800&year_end=2019&corpus=en-2019&smoothing=3
   See also The Break-Up Book Club - Page 221 Wendy Wax · 2021 But this morning when I wake up, I have something to look forward to. An actual reason to get out of bed and, I think, to bake.

2. is not to be known: I want to insist on the fact that in the future there'll still be no possibility of knowing that. https://books.google.com/ngrams/graph?content=is+not+to+be+known%2Ccannot+be+known&year_start=1800&year_end=2019&corpus=en-2019&smoothing=3

3. https://books.google.com/ngrams/graph?content=in+a+remote+past%2Cin+the+remote+past&year_start=1800&year_end=2019&corpus=en-2019&smoothing=3
   A Companion to Film Theory Toby Miller, ‎Robert Stam · 2008 Considering the primary formulation of Christian allegory by the Fathers of the Church, we can see it as a modality of allegorical interpretation addressed to given texts produced in a remote past under unknown circumstances.

4. connex: the meaning is correct but, indeed, this word form is obsolete

5. found in: "behind" seems more idiomatic

6. in the ancient French language: "old" is all right, but I see no reason for prescribing that "ancient" is outmoded.
   An Introduction to the History of Western Europe - James Harvey Robinson · 2018 Very little in the ancient French language written before the year 1100 has been preserved.

7. missing: "leave out" tends to mean "omit, ignore" ("leave out an 'm' in 'accommodation'", OALD), but "miss" is not better on that account and perhaps not proper. I'll change for "not used".

8. associated with: the SOED defines "associate v." as "3. b spec. Connect as an idea (with, †to)"; "†" means "obsolete".

9. it is: "it was" is merely another possibility; nothing wrong with "it is". See this for example: Advanced Monitoring and Procedures for Small Animal ... - Jamie M. Burkitt Creedon, ‎Harold Davis · 2012 It should be noted that many patients may develop ventricular fibrilation during a resuscitation attempt even when it is not initially present.
   You could say just as well "even when it was not initially present".

10. append: this is a perhaps not quite an appropriate term. Although the SOED has the definition "3 Add, esp. in writing.", from what I gather the items would have to be extra textual (whole text, paragraph, signature, etc.). I'll change for "use".

11. generic idea…: definitely awkward; had to be changed