Probably the best reason why tech support should not be outsourced is covered quite well in this article on Securityfocus.com.
I've done quite a bit of work with computers during my lifetime and worked with all kinds of helpdesks as a result. This isn't meant to be a racist or culturally biased statement at all, but I've found that the times when I've talked to someone who is a native english speaker have been the most productive and quickest to resolve my problem.
My first experience with an outsourced helpdesk was around 1996 or so when Acer outsourced their helpdesk to Costa Rica. I know it was Costa Rica because I spent so much time on the phone with Ramon that I knew much of his family, background, home town, and what he knew about the technology as well. Ramon wasn't bad actually, but the other idiots I had to talk to in order to GET to Ramon were competely useless.
I'm not sure when it is that this sort of investement is going to start backfiring on companies, but I certainly hope it's soon. I'm getting tired of calling a help desk and talking to someone in a far away land, with an accent so thick I can't understand him, but I did catch the fact that his name is 'Jimmy'. Not sure how many 'Jimmy's there are in Bhopal, New Dehli, or other Indian/Pakistani cities but apparently there are a few.