There could be a few different things at play here.
For your navigation (top navigation) I would definitely suggest you use "Home" as the link text for your home page link, not "cats".
If you are creating tons of internal contextual links on pages across your site by hyperlinking occurances of the word "cats" on a bunch of your pages and pointing them to the home page, this does not look at all natural IMO. If I built a search engine, this would be one thing that I would look for as an SEO footprint or over-optimization signal.
Contextual links make sense when they are used to point to a resource/reference where info for the post/article/content might have been obtained (this is typically an EXTERNAL contextual link, but could be internal) OR to link to some other post/ article that might explain something mentioned in the current post/article in greater detail (this could be either an internal or external contextual link).
Since your home page "should" be targeting your broadest, head terms and the deeper you click into your site, the inner pages should be targeting longer and longer tail keywords... It just doesn't make sense to me that your home page (which targets your broadest topic) would be referenced as a resource for or provide more detailed explanation for something you mention on an inner page (which should be targeting more specific, longer tail topics).
Maybe I'm just paranoid, but internal contextual links to other pages on the same site make more sense (i.e. seem more "natural") where they are inner page to inner page (typically linking to other pages deeper in the site or at least sibling pages on the same level, but not the home page).