If you have any https links on your site, those could be replaced by http links using something like sslstrip. Your site is now the weak link in the chain googl

If you have any https links on your site, those could be replaced by http links using something like sslstrip. Your site is now the weak link in the chain google->your site->linked site. Of course sites should be using HSTS to help prevent this, but if the user is visiting the linked site for the first time, HSTS can't protect them.