Running -9.6.1. I have a database created and owned by me, but cannot copy a table to my home directory. Postgres tells me it cannot write to that directory. The only way to copy tables to files is by doing so as the superuser (postgres).
When you ask the server to access the filesystem (e.g., via SQL COPY) it does so on your behalf but using its own operating system user. It makes no attempt to match the role that you are logged in as with a corresponding operating system user.
As Tom noted if you want to do things as "you" and not "the server" you need to perform them within a client (psql being the main one). In psql you can get COPY functionality via the \copy meta-command. The server sends its output to the client which then redirects it to some path on the local machine. If you run psql on the server you can access a home directory on the server.
Why is this
COPY naming a file or command is only allowed to database superusers, since it allows reading or writing any file that the server has privileges to access.
See above for why its the sever's privileges that matter.