Couldn't Have Couldn't Of

Phrases involving "________ have" crop up all the time.  Could have, should have, would have, and their ilk permeate English sentences, or at least they ought to.  However, all too often, the "have" somehow becomes an "of."  After my years of homeschooling, AKA undergoing extensive training as a grammar cop, I went to a public high school, thus for the first time encountering this particular error, which at the time shattered my poor innocent mind into a thousand tiny fragments.  What the...but...what, even...what were these people THINKING?*

Naive fool that I was, I thought the horror would abate with the passage of time - and, more stupidly yet, that this was some isolated incident.  Nope!  Not only does it still crop up, it does so a good 75% of the time "_______ have" should present itself.  Even worse, I've actually heard people PRONOUNCE it "______ of."

Of.  What the...!?  They don't even SOUND alike!**  Furthermore, "__________ of" makes no SENSE!  "I could of shaved the cat" means, literally, that "I could" belongs to "shave the cat."  It is Shave The Cat's pet I Could or something.  Please don't make me live in a world where strange activities keep domesticated abstract concepts.  My brain undergoes enough torture already.

"I could have shaved the cat," however, simply states that in the past you had the capability of rendering your pet feline hairless either because its coat had become inextricably tangled or because you're a sadomasochistic twit with too much time on their hands.   It's past-perfect of "could."  No, I don't know why past perfect is called "past perfect," but basically it's any past tense involving "have"  or "had" - "I have shaved the cat," as opposed to the regular past tense, "he clawed the bejeezus out of me."

Perhaps it's called past perfect because, unlike "could of," it actually makes sense.

*Answer: "They may not have been."  So far as I can tell, the best, or at least most widespread, high school survival method is to switch off your brain until the last bell rings.

**Well, sometimes they do, but I try really hard to pretend mumbling doesn't actually happen.