Bradley Headstone is a respectable, educated man who does a lot of service for his community as a schoolmaster. Yay, Bradley. But on the other hand, he is hopelessly insecure, awkward, and entitled. Boo, Bradley.
One of the first descriptions we get of him says that,
He was never seen in any other dress [than his formal clothes], and yet there was a certain stiffness in his manner of wearing this, as if there were a want of adaptation between him and it, recalling some mechanics in their holiday clothes. (6.1.28)
It's clear that Headstone is way too worried about the way people look at him, and this anxiety is what eventually leads him to try to kill Eugene Wrayburn, who insults him one too many times.
Earlier, we mentioned that Bradley Headstone was entitled. This quality comes from the fact that he has worked hard to raise himself up in the world and to earn people's respect. As the book tells us,
There was a kind of settled trouble in the face. It was the face belonging to a naturally slow or inattentive intellect that had toiled hard to get what it had won, and that had to hold it now that it was gotten. (6.1.28)
Unfortunately, Headstone feels that his hard work should also force someone like Lizzie Hexam to marry him. Or, in other words, he thinks that being a hard worker makes him a good person. And the fact is that this just isn't true. There are all kinds of hardworking people who are total jerks (we're looking at you, Ebenezer Scrooge).
Headstone just doesn't understand the difference between being a hard worker and being a suitable husband for Lizzie… which is what starts him on his path from mild-mannered academic to psychopathic would-be murderer.