Update object field of array in jsonb PostgreSQL

Solution 1 : jsonb updates based on jsonb_set

jsonb_set() cannot makes several updates for the same jsonb data, so you need to create an aggregate function based on jsonb_set() and which will iterate on a set of rows :

CREATE OR REPLACE FUNCTION jsonb_set(x jsonb, y jsonb, p text[], z jsonb, b boolean)
RETURNS jsonb LANGUAGE sql IMMUTABLE AS
$$ SELECT jsonb_set(COALESCE(x, y), p, z, b) ; $$ ;

CREATE OR REPLACE AGGREGATE jsonb_set_agg(x jsonb, p text[], z jsonb, b boolean)
( SFUNC = jsonb_set
, STYPE = jsonb
) ;

Then you can use the aggregate function jsonb_set_agg() in the following query :

SELECT jsonb_set_agg(r.data, array['educations', (a.id - 1) :: text, b.key], to_jsonb(CASE WHEN b.value IS NULL THEN array[] :: text[] ELSE array[b.value] END), True)
  FROM resume AS r
 CROSS JOIN LATERAL jsonb_array_elements(r.data->'educations') WITH ORDINALITY AS a(data, id)
 CROSS JOIN LATERAL jsonb_each_text(a.data) AS b
 WHERE b.key = 'major' OR b.key = 'minor'
 GROUP BY resume_id

And finally within the update statement :

WITH sub AS (
SELECT jsonb_set_agg(r.data, array['educations', (a.id - 1) :: text, b.key], to_jsonb(CASE WHEN b.value IS NULL THEN array[] :: text[] ELSE array[b.value] END), True)
  FROM resume AS r
 CROSS JOIN LATERAL jsonb_array_elements(r.data->'educations') WITH ORDINALITY AS a(data, id)
 CROSS JOIN LATERAL jsonb_each_text(a.data) AS b
 WHERE b.key = 'major' OR b.key = 'minor'
 GROUP BY resume_id
)
UPDATE resume cv
   SET data = sub.data
  FROM sub
 WHERE cv.resume_id = sub.resume_id

Solution 2 : break down and rebuild the jsonb data

SELECT jsonb_agg(c.data ORDER BY c.id)
  FROM
     ( SELECT resume_id
            , a.id
            , jsonb_object_agg(b.key,to_jsonb(CASE WHEN b.value IS NULL THEN array[] :: text[] ELSE array[b.value] END)) AS data
         FROM resume AS r
        CROSS JOIN LATERAL jsonb_array_elements(r.data->'educations') WITH ORDINALITY AS a(data, id)
        CROSS JOIN LATERAL jsonb_each_text(a.data) AS b
        GROUP BY resume_id, a.id
     ) AS c
 GROUP BY c.resume_id

see the test results in dbfiddle.