Learn English – have to say “want you to do” instead of “want you do”

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.