Scientifically speaking, why can't viruses be cured?
This depends on your definition of cure.
Many viruses can be prevented. Rotavirus, Polio, HPV, Varicella, Measles, Mumps, Rubella, Influenza, Hepatitis A & B can all be prevented with immunizations. However, many vaccinations are not 100% effective in preventing infection for two reasons: your personal immune system’s response to the vaccine, and mutation of viruses.
Your immune system, once exposed to a virus through infection or immunization, will create antibodies against a part of that virus (usually the envelope or shell of the virus). Over time, your antibodies may wane and you may be more susceptible to infection again. This is why we give booster vaccines, so that your immune system can “see” the invader again and bolster its defenses against it. For example, vaccination with one MMR shot offers 93% protection against measles, whereas protection goes to 97% with 2 shots.
Viruses also mutate (much like bacteria do when they become resistant to antibiotics) so that the body does not recognize them and attack with antibodies. They may also come in several common mutations or “strains,” so while you have immunity to one, you may be vulnerable to another. Some viruses mutate rapidly, like the flu, so we need repeat immunization against new strains and new mutations to keep up.
We tend to only vaccinate against the most common strains of a virus too, which is why you can get the Gardasil shot for HPV (which covers types 6,11,16, and 18) and still contract a less virulent strain of the virus. These multiple strains and mutations are also why it’s very hard to make a medication for viral illnesses (and why Tamiflu’s efficacy is modest at best for treating the flu). By the time a drug is made, the virus has mutated and it doesn’t work anymore.