Aw, I feel like I have to speak up for men aegyo. The reason why I like men aegyo is because it breaks gender stereotypes. In the West at least, mainstream society raises men to be emotionless, ambitious, macho men-beasts. If a guy is in any way soft, he's queer-bashed mercilessly, and I find that extremely damaging to men. I appreciate that Korean men don't seem to have this inhibition, and can be cute, and can think their food at a restaurant is so pretty that they have to take a picture of it---all of that, and still be entirely secure about themselves as men. On the flip side, I hate girl aegyo because it re-enforces this idea of women, or at least the ideal Woman, as being naive, innocent, pure, childish, and helpless. In which case I find girl aegyo to be extremely damaging to women.
In the conversation I had with my friend, we both agreed that aegyo does not translate well across cultures; it's definitely something that's specifically Korean, and needs to be understood within the Korean context. Granted, even within that context, I still find it annoying, but as my friend pointed out, aegyo is a result of the gender inequality prevalent in S. Korea. (Out of the 30 or so OECD countries, Korea has the largest pay gap between men and women workers; since women are expected to stay at home anyway once they marry, it's seen as a waste to invest in them by giving them a large salary.) I wish I could relay everything my friend said because it was interesting and awesome, but I won't be able to do her thoughts justice. =/