Postgresql – Unable to delete a referenced row due to a trigger on a referencing table

I ran into some problems in using triggers to ensure only deletions from cascading deletes:

CREATE TYPE status_type AS enum ('A');

CREATE TABLE parent(
    name VARCHAR(255) PRIMARY KEY
);

CREATE TABLE child(
    name VARCHAR(255) PRIMARY KEY
);

CREATE TABLE relation(
    childname VARCHAR(255) NOT NULL REFERENCES child (name) ON DELETE CASCADE,
    parentname VARCHAR(255) NOT NULL REFERENCES parent (name) ON DELETE CASCADE,
    status status_type NOT NULL,
    PRIMARY KEY (childname, parentname)
);

CREATE OR REPLACE FUNCTION prevent_deletes_when_status_A() RETURNS trigger AS $$
    BEGIN
        IF OLD.status='A' AND EXISTS (SELECT 1 FROM parent WHERE parent.name=OLD.parentname) THEN
            RAISE EXCEPTION 'Invalid DELETE';
        ELSE
            RETURN OLD;
        END IF;
    END;
$$ LANGUAGE plpgsql;

CREATE TRIGGER tr_onlycascading_fromParent
    BEFORE DELETE ON relation
    FOR EACH ROW EXECUTE PROCEDURE prevent_deletes_when_status_A();

INSERT into parent VALUES ('john');
INSERT into child VALUES ('doe');
INSERT into relation VALUES ('doe', 'john', 'A');
DELETE FROM child WHERE name='doe';

Why does this not work? I understand that it raises the exception message. However, the row in child should be deleted. Am I missing something here?

Shouldn't the row in child be deleted first before the delete cascades to the relation table, where only then would the trigger take effect?