A cat constantly licking its fur doesn't necessarily mean it has parasites. Licking is a normal behavior for cats, and there are many reasons why they might lick their fur frequently.

First, licking helps cats clean themselves and remove dust and debris. It's a form of self-care.
Secondly, licking their fur helps regulate their body temperature, making them feel more comfortable.
In addition, stress, anxiety, or boredom can also cause cats to lick their fur excessively.
However, the presence of parasites can also be a cause. For example, parasites such as fleas and lice can make cats uncomfortable, thus increasing the frequency of licking their fur.