A few years ago I was told not to use that word because, in addition to its negative meaning, it comes from Latin denigratus, past participle of denigrare, which means to blacken. Therefore, "to denigrate someone" would be "to blacken that person". Considering its current definition (see below) and the wish to be politically correct, I wonder whether the word has come to acquire any racist overtone.
The reason why I'm asking is because I was reading "Language Myths" a book by Laurie Bauer recently, and came across this passage which contained that word "...certain educational institutions denigrate the way certain ethnic minorities and lower-working-class children talk." Then I remembered I was once told not to use "denigrate" as it might be misinterpreted by some people.
denigrate - from Merriam-Webster
1. to say very critical and often unfair things about (someone)
2. to attack the reputation of, to deny the importance or validity of, belittle
EDIT (on Dec 17th, 2017) - This article, Dark Words Of Disapproval which Mari-Lou A mentions in one of the comments, shows very clearly the writer's feelings about this word, with very good arguments to bear him out.