Here's why:
* Transitive verbs require a direct object. They show an action performed on something. For example: "She threw the ball." (threw - transitive verb, ball - direct object)
* Intransitive verbs do not take a direct object. They describe a state of being or a condition. For example: "The dog slept." (slept - intransitive verb)
Linking verbs connect the subject of a sentence to a noun or adjective that renames or describes the subject. They don't show an action. They simply link the subject to the information provided after the verb.
Here are some examples:
* She is a doctor. (is - linking verb, doctor - subject complement renaming the subject)
* The flowers smell sweet. (smell - linking verb, sweet - subject complement describing the subject)
* He became angry. (became - linking verb, angry - subject complement describing the subject)
Since linking verbs don't involve a direct object, they are classified as intransitive.