When Elizabeth first met Darcy at the Meryton ball, everyone in the room agreed that he was the proudest, rudest man present. He only danced with Bingley's sisters and only conversed with Bingley's party. He refused to meet anyone new. He felt that the society was beneath him, even saying that there wasn't a single woman in the room that "would not be a punishment" for him to dance with. When Bingley encouraged him to dance with Elizabeth, Darcy replied that she was "not handsome enough to tempt" him. He further declared that he was "in no humour at present to give consequence to young ladies who are slighted by other men" (Ch. 3. Vol. 1).
Later, at Rosings, Darcy justified his behavior by saying that he was "ill qualified to recommend [himself] to strangers" (Ch. 8, Vol. 2). Later still, his housekeeper stated that what others misjudged as pride was actually reserve. Even if Darcy's behavior at the Meryton ball can be explained by a natural reserve among strangers, Darcy stepped over the social line by saying that the society was beneath him and that it would be a punishment for him to dance with anyone. He especially went too far in referring to Elizabeth as being "slighted by other men" because the true reason she was sitting out of the dance was that there were not enough gentlemen present for every woman to dance every dance.
Hence, yes, Elizabeth was justified in thinking Darcy to be a very proud, arrogant man. Darcy even later stated that he "was taught good principles but left to follow them in pride and conceit" (Ch. 16, Vol. 3). However, Elizabeth was wrong in allowing her observations of Darcy's pride to prejudice her into thinking that Darcy was "devoid of every proper feeling" (Ch. 16, Vol. 3). Contrary to Elizabeth's first impressions, we see in the book that Darcy is actually very kind, caring, and has a noble heart. We see this in his treatment of his sister, in his saving Elizabeth's reputation by forcing Wickham to marry Lydia, and even in his treatment of Wickham.
Well he was rather rude by calling her "not tolerable enough" but she does seem to take it a little too far. That's just my opinion, but it shows that she can be prejudice as well -- it's not only Darcy.