This article from the Mayo Clinic is a fairly easy layman terms read: https://newsnetwork.mayoclinic.org/discussion/forty-years-of-hiv-aids-will-the-epidemic-end/
"The reason why it is so difficult to cure HIV is that once HIV infects a person's body, it integrates into the host genome of several cell types. Those cells then hide in any of the lymphoid tissue, such as the lymph nodes, the liver and the spleen. And they lay there as what we call "latent" or "hiding", as long as the person is on HIV therapy. Anytime a virus does leave a cell, it gets taken care of by HIV therapy. But if the infected individual stops the HIV therapy, that latent virus will come back. To cure HIV, you have to eliminate those hiding viruses in the cells or that latent viral reservoir..."
There are two main reasons. The first is this above, regarding the "hiding" capability of the virus. Secondly, the virus' ability to mutate (or change its own form) rapidly means that targeting the virus itself is rather difficult. Essentially - while there are two main forms of HIV (HIV-1 and HIV-2), those main groups have thousands of mutations. Medicine can target certain markers that are similar, but even at that - the virus can mutate. This is what people in the tread are talking about when they refer to resistance and why stopping medication "to give their body a break" is not a good idea.
Mutation rate is not really easy to make layman term-ed, but here's an article that makes a good attempt.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4574155/
The best thing is that you are wanting to learn. Please continue to educate yourself -- and keep asking questions!
HTH