Can't git push to Bitbucket: Unauthorized - fatal: Could not read from remote repository

I can't push to Bitbucket and this is the error message:

> git push origin master:master
Unauthorized
fatal: Could not read from remote repository.

Please make sure you have the correct access rights and the repository exists.

Debugging, I receive this message when I ssh to bitbucket:

> ssh -T bitbucket.org
authenticated via a deploy key.

You can use git or hg to connect to Bitbucket. Shell access is disabled.

This deploy key has read access to the following repositories:
my-username/my-repository

The read access part of this message is suspicious.

PS: I know there are dozens of similar questions, but I couldn't find the exact error message here and only got the solution outside. That's why I'm self answering this to help others.

I was able to solve this using this suggestion:

1. Remove the SSH key from the repo. (Click on repo name > Settings > Access Keys)
2. Add SSH key to Account settings SSH keys. (Next to your avatar click Settings > Personal Bitbucket Settings > SSH Keys)

So, adding the keys under the repo only gives you a read-only access. For read and write access, you need to add your keys under your account.

To be fair, Bitbucket warns about the read-only access when adding the key to the repo: