結論

~/.nodebrew/src が必要だった

手順

#このようなエラーが出ます

> nodebrew install-binary latest
Fetching: https://nodejs.org/dist/v17.9.0/node-v17.9.0-darwin-arm64.tar.gz
Warning: Failed to create the file                                                                                                                                                          
Warning: /Users/azimicat/.nodebrew/src/v17.9.0/node-v17.9.0-darwin-arm64.tar.gz
Warning: : No such file or directory
                                                                                                                                                                                         0.0%curl: (23) Failure writing output to destination

download failed: https://nodejs.org/dist/v17.9.0/node-v17.9.0-darwin-arm64.tar.gz

#件のディレクトリを作る

> mkdir -p ~/.nodebrew/src

#うまく行きます

> nodebrew install-binary latest
Fetching: https://nodejs.org/dist/v17.9.0/node-v17.9.0-darwin-arm64.tar.gz
###################################################################################################################################################################################### 100.0%
Installed successfully