Killing pathogens is actually really easy. Some alcohol, bleach, or plain old fire will do the trick - the hard part is killing pathogens without hurting the infected person.

In order to kill a pathogen without hurting the infected person, you need to aim for something that the pathogen has but humans doesn't. With bacteria, there is an easy answer - cell walls. All bacteria have cell walls, and human cells do not, so most antibiotics target cell walls in some way (usually stopping bacteria from producing more cell walls, which stops them from dividing).

Viruses don't have a single common trait that's easy to target in that way. In addition, viruses don't spend most of their life cycle moving around independently like bacteria do - viruses will inject their DNA/RNA into a cell, and then that cell will be making more viruses. Finally, viruses are much simpler than bacteria, making them harder to "kill" without completely destroying them - which is harder to do without causing collateral damage.