That’s not entirely true. The body does learn to protect itself and it does mount an antibody response and does attack HIV infected cells.

But HIV is one of only three retroviruses that we know about that infect humans and cause disease. The body can’t fully clear any of them. Retroviruses aren’t the only viruses our bodies can’t clear, but the mechanism for why is different from other acute viral infections that hijack your cellular machinery to rapidly print out millions of copies of themselves, killing the host cell in the process. Retroviruses write themselves right in to your DNA and can leave zero trace of themselves on the surface of the cell they’ve infected for weeks, months, or years. Until your own DNA starts transcribing those viral proteins, it’s virtually invisible to your immune system. Once you’re systemically infected with any of the three human retroviruses, some (large) number of cells somewhere in your body will have the instructions to make more of that virus baked in to their biological operating system for the rest of your life. It’s why vaccines don’t work (at least on HIV). Vaccines don’t stop cells from becoming infected. They help your body kill off the infected cells before the infection gets out of control. But with HIV, really any level of active viral replication is “out of control” because it goes straight to places your immune system will never be able to see and immediately hides in cells you will have for the rest of your life.

It sets up a war of attrition that the body has no mechanism to win. With HIV that war involves the very cells the body needs to fight off viral infections, so over time the immune system slowly fails. With the other two retroviruses we can get, they can eventually cause lymphoma.

That said, the medications for HIV are incredibly effective both as a treatment and as a preventative. They completely shut down viral replication. There’s ones that stop HIV from entering a cell at all, one’s that stop it from transcribing itself from RNA in to DNA, one’s that stop it from integrating with your DNA, and ones that stop it from assembling new, functional viral particles. They can’t write it out of the DNA of already infected cells - again, some of which you’ll have for the rest of your life - but they can stop any new cells from becoming infected and keep viable viral particles out of the blood and sexual fluids.