I'm confused about 'want you to do (something)' and 'want you do (something)'.
Example:
"I want you to eat fish" instead of "I want you eat fish" or "I want that you eat fish".
Can anyone explain what is the grammar rule for this?
SHORT ANSWER:
The grammatical reason is that that is the rule with want.
LONGER ANSWER:
As discussed in somewhat more detail here, each English verb allows (the technical term is licenses) a limited set of possible forms in its complements. The only forms of clause which want licenses are those which employ a marked infinitive—that is, a verb in the infinitive preceded by the ‘particle’ to:
okI want you to eat fish.
okI want for you to eat fish.
The construction with a gerund/participle is sometimes acceptable:
? I want you eating fish when I return.
It is acceptable in this instance because the time adverbial when I return allows us to understand eating not as a gerund but as the participle in the marked infinitive progressive construction to be eating: you will be eating at a particular time. The to be in this construction has been conventionally deleted, in effect transforming eating into an adjective modifying you.
These are not acceptable:
∗ I want you eat fish. (unmarked infinitive)
∗ I want that you eat fish. (that + finite verb)
Those are the rules with want. Each verb has its own rules, and you have to learn them one by one.
You will find more discussion of licensing here, here, and here
∗ marks an utterance as unacceptable; ? marks an utterance as usually unacceptable.
Usage of WANT (verb) - a few guidelines
We don’t use want with a that-clause:
I want you to tidy your room before the visitors come.
Not: I want that you tidy your room
From Cambridge
New uses of the verb "want" are arriving all the time. Modern uses, some of them not yet registered in OED (Oxford English Dictionary) and other dictionaries, are shown in the following examples -
(+ that - clause) You want that I should lose both my lieutenants together? - A. Lejeune, 1986
From The New Fowler's Modern English Usage
When want meaning "desire" is followed immediately by an infinitive construction, it does not take for:
I want you to go (not: want for you to go).
When want and the infinitive are separated by a word or phrase, however, for is used:
What I want is for you to go.
I want very much for you to go.
Want in its meaning of "have need, lack" normally takes for: They'll not want for anything now that they've inherited his estate.
From The American Heritage® Dictionary of the English Language
Though American Heritage Dictionary opposes this usage yet sometimes this kind of usage is around the corner, though they are very rare (decision made by Google Ngram result)
I want for you to eat fish. (Here "want" means "desire", and it's telling my desire)