I think what grates most people about Wolfram is his inability to acknowledge the massive contributions that other people have made to his empire. As is noted in a comment down below, Mathematica is dependent on the efforts of dozens of extremely smart people, but Wolfram pretends as though he is the alpha and the omega.
Indeed, Wolfram seems to feel that if his name is on the software (which of course, it is), then it is his creation. The reality is that this is far from true. Additionally, as an above commenter pointed out, his arrogance is not limited to software but also his claims to scientific progress which are not rightly his own discoveries. In general he seems like a bit of a braggart. Photoshop is a fantastic piece of software, but the CEO of adobe doesn't go around throwing his weight. The same could be said of MatLab, R, pretty much any software really. The way he behaves is perhaps the norm in some industries, but in software (especially software backed by dev teams large or small), that kind of personality doesn't come off well.
Can you provide a specific example of a scientific discovery he claims is his own but was in fact discovered by someone else?