Why do I ground myself to the pc case if I can cause harm to my Pc?
Short answer: You can't cause harm to the PC case. You can cause harm to the internal components. So it's preferable to discharge to the PC case, to prevent yourself from discharging to the internal components.
Long answer: The PC case is a really big hunk of metal which doesn't really do anything. As long as it's metal, and all the pieces of metal are in contact with each other, they allow electricity to flow and thus helps shield everything inside from electricity (and radio waves, but that's another story).
OTOH, a transistor in modern integrated circuits have traces ("wires") which are only a few hundred atoms wide (some are less than 100 atoms).
When you discharge static electricity, you are transferring electrons from your body to whatever it is you touched (usually metal). Those electrons jump to the object, and because like charges repel and all electrons are negatively charged, they do everything they can to get as far away from each other as possible. Moving electrons = electricity. So once the static spark has jumped, there's a small electrical current generated throughout the object you touched.
Flowing electricity heats up the conductor it's traveling through (unless it's a superconductor). If the static discharge happens to hit a particular IC transistor, most or all of that electricity will flow through the "wires" in the transistor. Since the "wires" are only a few hundred atoms wide, it doesn't take much electricity to heat them to the point where they melt. At which point the transistor stops working. The case OTOH is a solid hunk of metal, so the electricity gets distributed over a lot more atoms (a much thicker "wire"), so the heating is much less. And even if there were significant heating, the case has no critical microscopic arrangement of the atoms which you care about.
Whether the case itself is grounded is irrelevant in terms of static. The number of electrons discharged via static is minuscule compared to the number of atoms in the case. So the overall effect the charge of those electrons has on the case is almost nil. That's why discharging static to a metal table let works. As I said, the point of case grounding is to protect
you from harm if a much bigger source of flowing electrons (110V AC mains power) somehow manages to make it to the case.