YSK it's either "should have" or "should've". "Should of" is incorrect
Why YSK?
The first person who typed "should of" probably heard of it in real life that was meant to be "should've", they typed "should of" online and readers thought that it's grammatically correct to say "should of" which is in fact wrong and it became widespread throughout the years on Reddit.
This is also a phonetic mistake. The same people also confuse "your", "you're", and "yore", because they've been repeating those words in a way that makes them sound the same when they do not.
Yeah, I’ve seen have in textbooks way more than ’ve and it’s baked into my brain... This mistake only happens if you hear the word before seeing it written.
It's because "should've" and "should of" are pronounced the same. It doesn't make sense because they're just writing what they hear instead of thinking "I'm using the contraction of the auxiliary verb 'have'"..
It's because you're a non native speaker. Should of is a phonetic mistake that can be traced back to repeating words you hear over and over again before you know what they actually mean