To be honest, I hate when anime's are dubbed, but mostly because of anime that was brought over to America being done horribly. I also hate that a lot of Japanese culture is removed from 'script' because people wouldn't understand them, which takes away from the show when looking at it from a plot standpoint. I mean, there are some anime like Nichijou, which if it were dubbed would be terrible just because a lot of the jokes are play on words which only make sense in Japanese and can't be explain using English. Things like that are what makes a lot of anime better subbed.
You might not realize it, but go back and look at shows you like, you'll notice that a lot of shows have instances where they make reference to a Japanese historical event, or a ceremony or play-on-words. These are what make the show funny or understandable. Sure if you don't understand what they are talking about it might get confusing, but it just takes a simple 'wikipedia' search to realize it and either understand or get a good laugh. Most good subs will include a quick reference at the top of the screen to tell you what they are talking about.
Obviously this isn't the only reason to not dub and anime, there are things like a lack of seriousness in America (you'll notice that voice actors don't do a good job of having a distinct voice for every character they do which in turns leads to hearing the same voice actors in different anime's and being able to point them out almost immediately). Now in this case there are some instances where an anime will get some pretty decent voice actors, but again, this depends on how serious they take the show they are dubbing and how much of a budget they have to spend. [Honestly, this is a very minor annoyance which can be overlooked]
My biggest problem out of everything is the censoring. In Japan, children can hear curse words and live their lives perfectly fine (by children I mean 15+). In America, most anime I've watched that are dubbed like to exclude the obvious words we cannot air on TV. 'Shit' 'Fuck' even sometimes 'Bastard' will be censored. I also don't like how they will cut out 'overtly perverted' scenes just because you can see their butt or the top of their chest (the best example of this is One Piece which was HEAVILY edited when brought over to the states, so much that any sign of cleavage was removed, and even entire plots were shortened and/or skipped because there was a major plot point that included overtly sexual themes they couldn't get around).
I come to tolerate that not every anime brought over will be kept exactly as it was written in Japan, but honestly, the voice actors sound far more 'passionate' with their lines in Japanese, I can read above a 3rd grade level so reading subs and watching at the same time are as natural as breathing (which also helps out a lot when watching other foreign movies/shows) and above all, it just feels natural.
Honestly it doesn't matter to me, I will always watch anime subbed, but I just feel like hearing the excuse (not saying this to anyone directly) "I would give it a chance, but I don't like reading subtitles." It just sounds rather ignorant to assume that since it isn't in English it isn't worth spending a few extra seconds to read something so you can understand what is going on even though it might be an amazing show you never thought you would've enjoyed.