Under certain server configurations and conditions, WordPress may require an FTP connection to retrieve and process core, plugin, and theme updates.  If you only see an option for FTP on this screen, do not despair.  You are not alone!  If a server is without the libssl2 library and PECL’s ssh2 package, the SSH2 option will not be listed.  While there are WordPress plugins that mimic this capability using various PHP libraries, implementations at the server level often provide better security and performance.

1. Download libssh2 (C library implementing SSH2 protocol)
2. At the command line, type the following

   # Unzip the libssh2 archive
   tar -xf libssh2-1.4.3.tar.gz
   
   # Change directory to libssh2 source
   cd libssh2-1.4.3
   
   # Compile libssh2
   ./configure
   make && make install
   
   # Install ssh2 PECL library
   pecl install ssh2-beta
   

After that, the SSH2 option should appear on the WordPress update screen.