Here I go, then.
1) Rose is a Mary Sue.
Yes, all companions have been somewhat bland. But, for me, Rose takes it to a new level because of the romance aspect she was specifically written for: as a character, she was bland and entirely intended to be a vehicle for teenage girls of the fandom to wank to (because, for some reason, the BBC believe nobody with a v****a can enjoy science-fiction unless there's some snogging because they completely lack empathy towards anybody who isn't them).
There's nothing to Rose that makes her any more interesting than any of the other companions; so what made the Doctor suddenly break his appearance of being completely asexual and choose a chavvy human teenager he'd known for all of a few weeks over somebody like Romana, who was not only the same species as the Doctor but was nearly equal and earned friendship through intelligence?
And then you've got the whole 'Bad Wolf' bollocks. Don't get me ******** started on that.
2) Rose is the source of the unnecessary and stilted romance in the series today.
Doctor Who survived for more than 40 years without romance even being a significant point; why add it now unless you know your character is so bland that she can't survive with modern audiences unless she becomes an empty vassal for wish fulfillment? She had no interesting personality and was extremely poorly written as a vapid stereotype of a council-house girl.
Donna garnered popularity based on her personality and friendship with the Doctor, showing that romance isn't necessary. Rose, however, seemed to be entirely based on romance and her popularity seems mostly based on this.
3) Rose was selfish and arrogant after Series 1.
As a result of the romance, Rose developed a really annoying and clingy attachment to the Doctor that left her with the impression that she owned somebody infinitely older and wiser than her. To Rose, the idea that the Doctor had a life and friends before her is unthinkable, resulting in her being an utter c**t towards former companions like Sarah Jane, who had not only done more with the Doctor in her time of travelling, but had also travelled with him for far longer.
Off the top of my head, I can't think of any other companions who had this much of a problem comprehending that they weren't special (perhaps with the exception of Martha, but she was a victim of the Doctor's bizarre infatuation with Roseykins and mostly just had a distaste for the way the Doctor fantasised about her non-stop) seeing as most of them had had a period of transition where they met the previous companions and were phased in (but Special Snowflake Rose didn't because she had the Doctor all to herself because truwuvbadwolfdoomsdaysofeels).
4) Rose became so obsessed with the Doctor that she felt no compassion for other people.
Of course, I've mentioned Sarah Jane, but I think the way Rose treated Mickey and her mum was atrocious. It seemed that she assumed everybody cared that she loved the Doctor so much that she could say or do anything and treat people like dirt in favour of a man she knew next to nothing about.