Macos – Operation timed out error when trying to SSH into local machine

Apart from indeed opening up IDENT port 113 towards the SSH client (so the server can try to connect to that), you might have some luck adding UseDNS no to sshd_config.

And I doubt it will help you (the client knows where to find the server, so it's not the 1st bullet, you tried the 2nd bullet, and the delays are longer than 10 seconds so the other bullets don't apply), but for the archives the OpenSSH FAQ states:

ssh(1) takes a long time to connect or log in

Large delays (more that 10 seconds) are typically caused a problem with name resolution:

• Some versions of glibc (notably glibc 2.1 shipped with Red Hat 6.1) can take a long time to resolve "IPv6 or IPv4" addresses from domain names. This can be worked around with by specifying AddressFamily inet option in ssh_config. [On the client; AvB.]
• There may be a DNS lookup problem, either at the client or server. You can use the nslookup command to check this on both client and server by looking up the other end's name and IP address. In addition, on the server look up the name returned by the client's IP-name lookup. You can disable most of the server-side lookups by setting UseDNS no in sshd_config. [On the server, AvB.]

Delays less than 10 seconds can have other causes.

• OpenSSH releases prior to 3.8 had an moduli file with moduli that were just smaller than what sshd would look for, and as a result, sshd would end up using moduli significantly larger than requested, which resulted in a speed penalty. Replacing the moduli file will resolve this (note that in most cases this file will not be replaced during an upgrade and must be replaced manually).
• OpenSSH releases prior to 3.8 had a flaw in ssh that would cause it to request moduli larger than intended (which when combined with the above resulted in significant slowdowns). Upgrading the client to 3.8 or higher will resolve this issue.

• If either the client or server lack a kernel-based random number device (eg Solaris < 9, AIX < 5.2, HP-UX < 11.11) and no substitute is available (eg prngd) it's possible that one of the programs called by ssh-rand-helper to generate entropy is hanging. This can be investigated by running it in debug mode:

  /usr/local/libexec/ssh-rand-helper -vvv

  Any significant delays should be investigated and rectified, or the corresponding commands should be removed from ssh_prng_cmds.

"Connection reset by peer" means the TCP stream was abnormally closed from the other end. I think the most likely explanations are that the remote server process handling the connection has crashed, or else some network device (like a stateful firewall or load balancer) has decided to interfere with the connection.

You need to debug this on the remote server if you can. sshd logs through syslog, and on a typical Unix system the log entries will be in one of the files in the /var/log directory. If you're lucky, sshd will be logging something every time it drops your session.

If you have root access on the server, you can run a debugging instance of sshd. Become root and then run:

/path/to/sshd -ddd -p 1022

This will run an instance of the SSH server which will listen on port 1022, accept one connection, and print debugging information to your terminal. Run your client as usual, except specify port 1022 as the port:

ssh -p 1022 user@host

The debugging information printed by the server will hopefully make it clear what is happening.

Edit: The server output indicates that the server isn't crashing or deliberately closing the TCP connection. Something else is causing it to close. I would take a look at any security software installed on the server which might monitor TCP sessions, as well as any firewalls, load balancers, or similar network hardware which might be part of the local network.