For someone who wants to present himself as being such a bigly strong man, he sure doesn't handle himself well when a 78 year old woman is 'mean' to him. As the majority of critical commenters say, he comes across as a whiney toddler throwing a tantrum.
Note that Stahl has spoken openly about a meeting she had with trump, in which he explained why he came up with and continued to use the 'Fake news media'-slur.
I'd be surprised if that was part of trump's hatred of her, but you never know...