I do think Corbyn gets a hard time in the media, but his problems IMHO run far deeper than that. I will preface this by saying I am not a Tory voter- I'm a floating voter. But won't be voting for labour.
Personally, I don't entirely buy all the "genuine, honest, man of principal" things trotted out. I think there are some things he does genuinely believe and campaign for. However, he is not the messiah/saviour that so many Labour supporters see. Some of them would practically canonise him! I find it bizarre.
Look at the anti-semitism debacle and how quickly Shami Chakrabarti got into the Lords following her very favourable support, it just looks fishy. The whole Ken Livingstone affair does not look good. Over brexit he said he was remain but was virtually invisible and gave very weak support when he did deign to speak- which I think suggests he said one thing in public and another in private. Man of principle? Only on certain things would be my assessment.
He has been a professional rebel as a backbencher but doesn't like it when others do the same. He does not have good leadership skills and, mostly, does a poor job of doing what opposition leaders should so- holding the government of the day to account. It's all quite chaotic.
Added to this, he surrounds himself with people like McDonnell who strike me as untrustworthy and sanctimonious. And Dianne Abbott who has an unfortunate knack for sounding utterly patronising (as well has her tendency to hypocrisy). Momentum in itself has a very unpleasant side to it. I find it hard to articulate, but I find this wing of the party deeply unpleasant, they make me very uneasy.
Then look at the policies. Some policies are good, but they aren't costed properly. Not that Labour are unique in that- but when your ratings on economic competence aren't great, I'm afraid that you need to be more accurate and show that the perception if incompetence is not well deserved. Perhaps not fair but it is reality! One example for me is the revenue raised by their proposed changes to CGT has been spent several times over. Then we are told that the previous policies were only "suggestions" of how they "could" spend the money. Again, it seems chaotic.