The vast majority of people don't do Latin at school!
Someone above said it ought to be obvious because it's short for et cetera.
But first, not everybody knows it's short for et cetera. I only learnt that as an adult. When I was a child, I heard people say "et cetera" out loud but would probably have assumed it was spelt "excetera" because the t is very weakly pronounced. I think some people assume it is "Ec[k] Cetera" which would make more sense to shorten to ect than etc.
Secondly, even if you know that it is correctly et cetera, the letters ect are also in order in that phrase. People may be thinking "Et Ce Tera".
I have always spelt it correctly as far as I know, but I was a big reader and so spelling comes easily to me, I am more likely to get the spelling than the pronunciation right for lots of words. To me, ect just looks wrong so I would automatically correct it, but it is possible that people get it wrong because they are overthinking it, rather than that they are underthinking it.
I also just think it's snobbish and rude to look down on people because they don't happen to have the same abilities or lfie experiences as you. I don't know the correct spelling of etc because I have some kind of superior intelligence/knowledge, I just happen to find it really easy to memorise and store the spellings of words to the point I don't even really have to think about it.