I had to join just to add to this. I haven't paid the respect to other members, veteran or not, who already shared their opinions, so I'm sorry if I echo things.
Atheists and Religious folk get upset over very different things. When you tell a religion person that they are wrong, you are subsequently telling them they are delusional and the people who they respect most (family, friends, mentors/priests) were delusional as well. So that's where that insult and defense comes into play. Which is why so often when you tell somebody their belief is silly/wrong, they default with being content with faith/baselessness, for the sake of the good feelings something allots them. This allows them to honor those who they respect when they were taught such things. So that's religious folks.
Atheists are different in that they hold no biases for anything beyond evidence, and generally would lack respect for whom they learnt if the teachings seemed fantastic or unrealistic in some way. So when a religious person says something fallacious, the atheist will want to know why they believe such things. And most often the answers given are not up to snuff; they are not coherent or reasonable. So to a person with no biases, being told something which clearly has its holes is frustrating and unacceptable.
I'll give you an example. Lets say you knew everything there was to know about rocket science or dandelions. When somebody comes up and says something explicitly incorrect about rocket science or dandelions, you would speak up and say, "Throughout my years of research, what you said is incompatible with the facts I've come across. I would like to cross examine your views. If your views don't review well, I'm in line to tell you you are wrong and have you accept it, OR I am in line to be upset with the delusion you're spreading about my passion (dandelions / rocket science), and must insist that you immediately stop the charade."
If somebody is wrong, and you had factual reasons to explain why they are wrong, or people are pretending to know that which is not yet known for the sake of getting to showcase how much more enlightened they are than other thinking people, then you are right to speak up because THAT'S how you've obtained the knowledge you have, so far. This is not meant to insult, but it's subsequently offensive to those who are not use to being questioned, and of course offensive to those who value truth and rationality.
The question needs to be asked differently when wondering why the two cannot get along, because it infers they get upset over the same reasons--that reason being that they just want everybody to agree with them, or something. It's not the case in either position. I could go on but this comment is long enough.