to copy column from one table to another in psql
You don't need an insert here, as this is about adding new rows. You want rather to make an update. Something like
create table a(id int, v varchar(10));
create table b(id int, v varchar(10));

insert into a
select 1, 'a'
union all
select 2, 'b';

insert into b
select 1, null
union 
select 2, null;


update b set v = a.v
from a where a.id = b.id;