I enjoy debating things (hence I am on this site) and I do not hate people who disagree with me but instead I value their contribution to my learning. Hatred in my mind is reserved for only the very worst criminals and absurd religious doctrines such as the denial of life saving medicine to children.
If it were impossible to disagree with someone without hating them, then nobody would have any friends. Everyone disagrees about something with someone else. Nobody agrees completely with everyone. For example, just because my friend and I have different political views doesn't mean that we hate each other. If we did, then we wouldn't be friends.
My friend loves the color red. I hate the color red. We're friends. I disagree with my friend's religious beliefs, she disagrees with mine. We're still friends. Unless you're Westboro Baptist Church or a group like the KKK, I believe it's quite possible to not hate someone if you disagree with them.
There's a lot of anger being thrown around in the religious arena. A lot of people wouldn't consider it an arena, but there is a battle going on. All religions are fighting each other and all religions are fighting Atheists. There are Theists who understand Atheism well enough to leave it alone just as there are Atheists who understand Theism well enough to leave it alone. However, many insults, slurs, and other ethical, intellectual, and on occasion physical attacks are still being thrown about, from all sides. So, as I am an Atheist, not a Theist, let's focus on the side I'm more familiar with.
Actually, this question is relying on a false statement. Atheists don't hate Theists. Most Atheists see religion as a delusion, true, but we also respect other's beliefs. We'd rather not have those beliefs be the main driving force of those in power, but we don't mind if you worship God, Allah, Thor, or Buddha. If it makes you happier in life to believe that there is a being with more power and more knowledge than you, who has a plan and wants you to be happy with him, then most of us are all for it. We won't try to stop you from pursuing your own personal happiness, wherever you find it.
Unfortunately, these Atheists aren't as vocal as the ones people mostly encounter. The loud, insulting, and sometimes dangerous Atheists are the most pronounced. There are a few like The Thinking Atheist from YouTube who are benevolent and just want to reveal our truth to any who will listen. Then there are those like The Amazing Atheist, also on YouTube, who are a little more insulting than most but trying the same thing. He, just like The Thinking Atheist, is just trying to get people to understand what we know and why we see it as the truth. One thing you have to understand, though, is that these two, as well as a lot of the others on YouTube and similar social networks, are not just being informative but must also be entertaining. Without the entertainment factor no one would sit through the boring parts where they actually explain their position.
As for why the truly dangerous and hateful Atheists hate Theists, I really can't say. Why do the truly dangerous and hateful Theists hate Atheists? There are two sides to every coin, but the answer to your questions doesn't always have to be found on the other side. Sometimes, it's a lot closer to home than you might think. Search within your own group, find the ones that hate the opposing group, and ask them yourself. Maybe you'll get your answer.