Why is there a general dislike for asian universities? I had intentions of applying for higher education in Korea or Japan, but I was told many times that "Doing PhD in an Asian university is a career suicide".

Why is that?

My field is cognitive neuroscience, and to be more specific I'm interested in a  PhD in Cognitive Neuroscience at the Seoul National University.
Maybe because they're less well known (in the US and perhaps Europe too)...?

In the US, for instance, everyone knows about Harvard, Yale, MIT, etc. They probably also know about Oxford and Cambridge. But then, few outside of academia will be able to recognize the quality of programs at the other European universities, such as ETH, EPFL, TU Munich, the University of Copenhagen, or, in the case of Asia: at the University of Tokyo, the National University of Singapore, the University of Hong Kong, the Korea Advanced Institute for Science and Technology, etc. Less recognition means general distaste/disdain.

But then, if you ask people in the right niche, they will give much better evaluations. A physicist will know that the University of Tokyo has a very good (indeed, one of the best) physics department, their research leading to quite a few Nobel prizes. A mathematician would likely recognize the Kyoto University Research Institute for Mathematical Sciences (again, a few of their faculty members have been honored with Fields medals). A computer scientist might know about the National University of Singapore's computing programs. A biomedical scientist would probably have good things to say about the University of Hong Kong, and so on. There's quite a lot of top cadre research going on in many Asian universities!

Moreover, it can even depend on the subfields concerned: for example, in general computer science, the Institut national de recherche en informatique et en automatique (INRIA; the French National Institute for Computer Science) might not pop up as a big name; in my subfield, though, it's a very renowned place. The best advice: ask someone who knows about your field very well!

(Of course, I know very little about SNU, and nothing about cognitive science. But someone has to know.)