The female mosquito is not considered a parasite,although it needs our blood for reproduction.Why?
A parasite is defined as an organism that lives on or in an organism of another species, known as the host, from the body of which it obtain nutrients. Parasites are categorised as ectoparasites (that live on the body of the host) and endoparasites (that lives in the body of the host).
Female anopheles is not a parasite because it does not bite human to get its own meal. Both male and female mosquitoes feed on plant nectar, fruit juices and liquids that ooze from plants. Female anopheles bites human to get blood meal to nourish its developing fertile eggs. Their eggs need some iron requirement. So, they need human blood for reproduction. Their time frame in/on the body surface is also not enough to categorise them as parasites. They additionally do the job of a vector. The vector transmits parasites to the host. Female anopheles are vectors that transmit Plasmodium vivax, a malarial parasite to human body.
The mosquito does not need blood to reproduce, they lay their eggs in water. Female mosquitos only feed on blood. A parasite is a creature that cannot live/breed without completly depending on another being. Mosquitos are not considered parasites just as lions and other predatory animals are not parasites.