Interesting thread.
The term "host" has no bearing on the type of relationship, it only suggests who approached who. When baby clownfish drop from the plankton at the surface to the sea floor upon their metamorphosis, they almost immediately seek out an anemone. They approach an existing anemone.
So for the chicken & egg analogy...the anemone came first and the clownfish visits it (and stays). The anemone hosts the clownfish.
Now on to relationships...we know the clown/anemone thing is symbiotic because they benefit each other. The greatest benefit clowns bring to anemones is protection from butterflyfish which will eat an unprotected anemone pronto! In a parasitic relationship only the parasite benefits, not the host (and see, the parasite approaches the host not vice-versa), and often to the host's detriment. There are other types of relationships too, like commensal.