I was told not to mess with the core files. Also, I don't want jQuery to load on every single page.
Get rid of the plugin/theme that's causing jQuery to load :) jQuery is shipped with WordPress doesn't mean that it's loaded every time by default, it's being loaded by a theme or plugin that you're using. Look for a call to
Most themes will, by default, include Jquery.
If you REALLY don't want it to load, put this in your Functions.php file (in the theme)
Or find and put in comments (add // in front) these lines.