How do I silence the HEAD of a curl request while using the silent flag?

Try this:

curl --silent "www.site.com" > file.txt

If you wish, you can use the shorthand -s.

You need to use --silent with two dashes. Your “option” -silient (sic!) enables the -s, -i, -l, -e, -n and -t options.

-i is what includes the HTTP header.