There are a number of themes that are controversial (provoke debate, are unsettled, polarize opinion, or are reflected by a range of positions) in psychology. One example involves nature vs. nurture: some people think that much of our language ability is innate, while others think that very little is innate. I've fleshed this example out a little bit as an answer below.
I will eventually gathering data on just how controversial certain themes are, as a step towards investigating what the various factors are in such differences of opinion. Until then, or a starting point, I'm happy with opinions about what you think might be controversial.
Suggestions from various subfields of psychology are welcome, but I'm looking more for issues that most people with a psychology degree might be able to form an opinion on, rather than something that is highly controversial for a small group of specialists, which the broader community won't have much interest in.
Currently I have a list of themes that I think are controversial, but I was wondering what people in the field in general think. In other words, there might be something obvious that I've missed, and this seems to be a reasonable way to reduce the probability that there is.