Perhaps because people who described themselves by using this term were extremists (or at least, viewed that way)?I agree with you, and I would feel slightly insulted too but I'd have already judged the person who'd used it anyway so I wouldn't feel too bad.
What I meant was, how come it has become an insult when calling it somebody literally means that the accuser is not alert to injustice and by using it an insult implies they wear that as a badge of honour. It's like the unintentionally ironic use of 'snowflake' by people who are the ones getting wound up by people who won't accept use of something that was previously acceptable, therefore themselves are 'snowflakes'.
Calling somebody woke says much more about the person saying it than it does the person it's being aimed at.
Remember this term originated in the USA where there is so much polarisation on political matters, it's unreal.
I'm not a fan of Americanisms coming into the English language.
The term woke tends to be used to describe someone who goes 'over the top', or perhaps to 'over compensate' an injustice, etc. It's not used as a term to refer to an ordinary person who acts in a rational manner.