He DOES NOT HATE YOU, quite the opposite!
I have been there with ds, and there's a slightly smaller gap between him and dd. I would say he would be going through tantrum stage anyway and is jealous of the new baby but instead of taking it out on his sister he is taking it out on you (I personally think its easier like this, I think in practical terms it could be a nightmare if I had to be supervising him near dd 100% of the time) As a PP said you were his "anchor" and now he has to share your attention.
Remember that tantrums are perfectly normal, their little bodies get pumped with adrenaline and it needs a release soit's nothing personal(hard to remember when you are listening to them scream, I know!). He is testing all the boundaries to make sure you still love him no matter what, even when he misbehaves.
Once the tantrum has started I think the best thing is to let them cry/scream it out but tell them you can see he is upset and you are there for him once he calms down (don't leave him alone while he cries, you can sit on the floor close to him for example, don't leave the room unless necessary) After he calms down then you can give him a cuddle talk to him about what he wanted, why it wasn't possible, what the rules are, etc.
It is also important to phrase things carefully using "we" as in "we don't hit" rather than "don't hit me", so that it sounds more "universal law" rather than something directed solely at him.
I would also try to get some 1 to 1 with him if you don't already even if its 10 minutes at a time, with no distractions at all (phone, etc.) and tell him it's special ds and mummy time (I even "tell" the baby, "sorry dd, you can't do this now it's just for ds and mummy"). Dd is now 9 months and I would say Ds is back to his normal self, and he not only had a new sibling, but has gone from being with me all day to starting school for 5 hs a day since September, so I would say he is done quite well really. I had days when I shouted at him and was a lot harsher than I would have been before, so he's done better than me really!
Just remember he loves you and he needs you more than anyone else, he will get there with a bit of time and reassurance.