I was wondering, can two people DESTEST each other on sight? Isn't it a word a bit too strong for the situation? Should I assume that they destested each other even before they spoke to each other?
You asked what it means, not whether or not it's possible! I agree that it seems a little strange (especially now that you've got an extra "s" in "detest") but I suppose it's no more unlikely than "love at first sight." Are you quoting from something? Is there more context? Context is always helpful.
The common phrase is 'They detested each other at/on first sight'. ie from the first time they saw each other, they were in an ongoing state of detesting each other.
I don't think that's impossible, although it's not a common experience. In addition, such phrases do not have to be taken literally. Perhaps they spoke a few words, or spent a little time together,