、。
My father won't let me have a dog.
Literal
Father [topic-は], me [subject-が] dog [object-を] keep [nominalizer-こと] [object-を] permit [for me-てくれない] [explanatory-んです].
許してくれない — 許す (permit) + てくれない (won't do for me). The ~んです at the end adds an explanatory/slightly frustrated tone, as if the speaker is venting.