Hint: Parasite is an organism that depends on other organisms for its growth and survival. The parasite leaves in or on the host and obtains support, nutrients, and other components that may even cause disease or death of the host. Without a host, a parasite cannot live, grow, and multiply.
-A female mosquito though feeds on blood and in the case of Anopheles mosquitoes it is even a cause of malarial disease, still is not considered as a parasite because the mosquito feeds on human blood for reproduction and not for its survival. Also in the case of malarial disease anopheles female mosquito is just a carrier and is not the sole reason for the disease.
-Female mosquito feeds on human blood for the nourishment of off-springs during reproduction. In fact, unlike a parasite the female mosquito does not leave in close association with the host, they just suck the blood and leave the human host.
Male mosquito feed on plant nectar because of two reasons; first being they have a blunt proboscis and 2nd is they do not provide nourishment for the development of offspring. So even male mosquitos are not considered as parasites.
Note: A parasite spends an entire lifespan or at least a considerable life span on or within a host and during this time it entirely depends on the host for its food, nutrition, and habitat. A female mosquito on the other hand just associates itself with the host for a few seconds, sucks the blood, and detaches itself from the host. Also, the blood sucked by the female mosquito is not at the expense of the host and does not cause any harm directly to the host.