Why is a pradicate can be a verb phrase? I thought the pradicates cannot include in the phrases ...

First of all, the word is "predicate."

And, yes, a predicate can be a verb phrase.

A simple predicate is simply the main verb (which follows the subject).

A verb phrase is that main verb (the predicate) and ALL the words that follow it.

Explanation:

S V O

Ex. I ate the pizza.

[ predicate ]