The filter is different than a category.
A category is a link to a list of a group of products.
A filter is a way to filter/reduce that list of a group of products.
So, you must have a list of products to apply the filter to. Therefore, the filter will only "work" on a page with a group of products.
Your index page
does not contain a list of products. It contains a list of blog posts. So there is nothing to filter.
I hope that makes sense.