To find out why Paddy Maguire does not like being called mean by his wife in "The Fur Coat," we have to consider the context of the remark. Paddy comes home after receiving a promotion (and presumably a raise in pay), and in response Molly requests a fur coat. Paddy, who still admires his wife, immediately agrees. They then discuss the cost of such a coat, and it becomes apparent that Molly will only be able to afford a relatively low-cost fur coat, but Paddy encourages her to go ahead and get it.
Even after her husband's agreement, though, Molly continues to ruminate. It is clear that she herself is double minded about whether it is right for her to purchase the coat. She breaks off the conversation several times and brings up the subject again, sharing her doubts with her husband, who is trying to focus on his work. At one point she accuses him of not wanting to get her a fur coat, and then she calls him mean. This remark offends him. Whelan writes of Paddy,
He sat miserably at his table, cold with anger. He murmured the hateful word over and over, and wondered could there be any truth in it.
To grasp why the word offends Paddy so much, we need to discern what his wife meant when she said it. Here it seems that Molly is referring to Paddy's unwillingness to spend money. His wife is accusing him of being so frugal as to be unwilling to consider her desires. This is, of course, not true, because as soon as she broached the subject of the fur coat, her husband immediately agreed that she should have one. Paddy gets so upset over this remark because his nature is the opposite. He is not mean; he is generous and kindhearted.