There are two main reasons why mosquitoes are not vectors for transmitting the HIV virus.
The first is the fact that the AIDS virus does not survive for very long outside the confines of the human body. It will only survive for about one hour, and that is why HIV cannot be contracted from toilet seats, mosquitoes, etc.
The other reason is that the mosquito does not actually inject blood that it has extracted from one animal into another animal.
Instead, the mosquito injects saliva into the skin in order to prevent coagulation of the blood, but does not actually inject blood that may be tainted with HIV into another animal.
It is a very good thing that mosquitoes cannot transmit the HIV virus, or else a very large proportion of the Earth’s population would be HIV positive.