I mainly despise, rather than hate the dm for its terrible, dishonest journalism. When you read an article in the dm, they will often miss out really important facts, or slant them in a disingenuous way to deliberately imply something for their own political agenda, which is simply not there in the original story. You only need to read the article about the same story in the Telegraph, Times, Spectator or other right wing publication, ot see that.
That is OK, if you are doing an opinion piece or a polemic. If you are purporting to be reporting the news, then it is abysmally dishonest journalism and it brings the whole profession into disrepute. It does its readers a disservice by not reporting the full truth as best it can, and it is cynical and wrong. Hating the DM it seems to me, has nothing to do with its political stance - the Telegraph is far more right wing than the DM in many ways, and it is a good newspaper - it is to do with the DM's shockingly cynical approach to journalism. I know it sounds a bit pompous, but when I think of really brave journalists in parts of the world who risk their lives to get the truth out to people (and it really does happen, you only have to look at the Rory Peck awards to see how dangerous it can be to be a journalist in some place), I just can't help feeling that the cynical manipulation of the news is a real betrayal of journalism, tbf. And that's mainly why I find the DM disgusting, not because of its politics. HTH.