An argument about emotions can be good or bad like any other, a simple "just because it offends me" is a bad argument because I can be offended by censorship and find your attempt to censor offensive. However a "Currently that word has been embraced by people with a certain mindset, thus by using it you're giving those people more validation on their beliefs as they think you're one of them" is a very clear argument as to why certain words can be hurtful socially.

My culture is not a costume to me is sorta a weak argument, think about what people dress as for custome parties: Pirates, Ninjas, Vikings, Nuns, Nurses, etc... Most costumes are either of something that doesn't exist or a culture (and sometimes both). However diminishing someone's culture to just the clothes is offensive regardless of culture, and exalting a problem in that culture as part of your costume is also offensive. For example, as someone born in Argentina I wouldn't be offended by someone dressing as a Gaucho, if a friend of mine wanted to dress like that for a costume party I would even lend him my mate. But I can see people getting offended by someone dressed as a soccer player with white powder under their nose (although me personally would just laugh it off, I can see that as being something someone takes offense with).