I agree that people over-use the word 'rare' on eBay.
But if I may, I would like to play devil's advocate for a bit.
Imagine the collector world before eBay. Imagine an item of which, say, only 100,000 were made.
In your pre-eBay lifetime you may only run across a couple of them in antique stores. They are considered rare.
Fast forward to eBay. There are no more, though possibly fewer of these items around. But because eBay exists, those that are sold often end up being sold there, for all the world to see instead of spread out among thousands of antique stores.
The item has become incredibly easy to find. But is it any less rare than it was before?
Excellent summary if then one is to take the stance that an item is therefore determined to be rare according to availability. We are therefore determining the word availability as being one's ability to achieve possession of an item.
Therefore the item is rare due to it's availability rather than it's quantity pre-eBay.
Likewise post eBay has reversed this by making the quantity available to all and therefore quantity determines rareness.