"Please open the gate."
Why don't they use the intransitive verb ? Shouldn't it say 開いて下さい？
Intransitive verbs don't have an object (target of the action), and transitive verbs do.
Here you don't ask the door to open by itself, but to someone to perform the action of opening on something (the door), and that something is the object. So, as the verb (open) has a target/object (door), it is transitive (because it transitions the action into the object)