So you are trying to do a fulltext search but your searches for “cat” or “dog” always return zero results, even though you have articles all about cats and dogs. By default the minimum search text length for full index searches is 4 characters, anything less than that returns nothing, zip, nada, jack-all. You need to change the minimum word length.
This can throw people using something like Magento whose product types or names are short, such as “bag”,”cup”, or “mug”. The problem isn’t actually in Magento but a server setting. You might be kind of stuck if you are using a shared hosting environment – you can contact your hosting service and ask nicely.