Open an URL in Safari with Private Browsing
Safari does not have similar command line options like Google Chrome, however, here is a way to roll your own:
In Terminal, run the following compound command:
touch safari; open -e safari; chmod +x safari

Copy and paste the example AppleScript code, shown further below, into the opened safari document, then save it.
You should then move the safari shell script to a directory located within the shell's PATH.
I moved it to /usr/local/bin, e.g,:
sudo mv -v safari /usr/local/bin/

Now from Terminal I can open a new private window for Safari.  Typing just the executable's name without any arguments shows how it can be used e.g,:
% safari
Missing Arguments!...
Examples:
safari https://www.example.com
safari -private
safari -private https://www.example.com
%    


Notes:

As coded, the example AppleScript code is focused on opening a new private window, however, as you can see it can open a normal new window to the provided URL too. For the new private window, you can open it with or without passing it a URL.
As coded, the example AppleScript code only allow for one URL to be passed at a time. Additional coding is required to allow passing multiple URLs.


Example AppleScript code:
#!/usr/bin/osascript

on run args
    
    if args is {} then return ¬
        &quot;Missing Arguments!...&quot; &amp; linefeed &amp; ¬
        &quot;Examples:&quot; &amp; linefeed &amp; ¬
        &quot;safari https://www.example.com&quot; &amp; linefeed &amp; ¬
        &quot;safari -private&quot; &amp; linefeed &amp; ¬
        &quot;safari -private https://www.example.com&quot;       
    
    set newPrivateWindow to false
    
    if item 1 of args contains &quot;-private&quot; then
        set newPrivateWindow to true
        if (length of args) is not greater than 1 then
            set theURL to missing value
        else
            set theURL to item 2 of args
        end
    else
        set the theURL to item 1 of args
    end if
    
    tell application &quot;Safari&quot; to activate
    delay 1
    
    if newPrivateWindow then
        tell application &quot;System Events&quot; to ¬
            keystroke &quot;n&quot; using ¬
                {shift down, command down}
        delay 1
        openURL(theURL)
    else
        tell application &quot;System Events&quot; to ¬
            keystroke &quot;n&quot; using ¬
                {command down}
        delay 1
        openURL(theURL)
    end if
    
end run

on openURL(theURL)
    if theURL is missing value then
        return
    else
        tell application &quot;Safari&quot; to ¬
            set URL of ¬
                current tab of ¬
                front window to ¬
                theURL as string
    end if
end openURL