Question

why dont antiviral medications also kill host cells?

Answer 1

antivirals consist many different drugs and components with many different mechanisms and structural designations . the idea is simple - strike in sites specific for viruses... For example;
acyclovir - for herpes takes advantage of the fact the viruses utilize a different thymidine kinase (for connecting the T's to the DNA) - thus it does not affect and or has minimal to no damage to human cells and body structures
like the medications for flu; amantadine and Tamiflu construct knowledge from some basic science attributions about the life cycle of the flu cells and how it travels from one cell to infect the next surrounding cells. The medicines target to viral proteins - neuraminidase thus crippling its infectivity
same ideas for medications like haart - highly active antiretroviral therapies for hiv learn the viruses - isolate where it differs and hit there where the heart of the virus infects other cells.

Answer 2

welcome to openstudy, agreed^