It's not without its stellar performance reputation and extremely consistent build quality that the EF 70-200 f/2.8isII has found it's way into just about every Canon professional's bag on the planet. From this point it's frequently stated as being a "most-used" lens. So what's happening for you?
There is a chance that it is a very rare poor copy, it's in serious need of AFMA adjustment, there is comprehensive user-error or the unlikelihood of you being a malicious troll. I doubt this is the case!
Read up on AFMA (auto focus micro adjustment in case you were unsure) and do the adjustments as a start point.
This tends not to be a lens that disappoints. If you bought second hand, there are the occasional copies that have been dropped/damaged and badly repaired, then dumped into the hands of a trusting, unsuspecting buyer. As with anything pre-owned, YMMV.
You can afma easily using the af beep method.
Manual focus a subject with 10x live view. Preferably a subject some noticeable detail
Set focus to manual.
Set af confirmation to beep.
Adjust afma back and forth and press the shutter button on between each time, noting the point where the beeping stops. Then average the result.
Eg if it stops beeping at -3 and 3 then your lens is spot on.
If it stops beeping at -6 and -2 then set your afma to -4.
Repeat a few times for greater accuracy.
It is quick. Simple and free. I calibrate all my lenses this way. It works great for me. Better than using software