Iri is the kind of demon the King of Knights fears. And also loves. Celtic legend doesn't exactly make the two mutually exclusive.
I think she's talking about her inheriting Kiritsugu's cold calmness in battle & comforting herself that she's at least as lovely as her mom.
She definitely inherited that devilish cool-headedness...Illyasviel... poor thing ... It would be a good thing if she had just inherited Irisviel's lovely appearance...