Attribute inference - the process of analyzing publicly available data in order to uncover hidden information - has become a major threat to privacy, given the recent technological leap in machine learning. One way to tackle this threat is to strategically modify one's publicly available data in order to keep one's private information hidden from attribute inference. We evaluate people's ability to perform this task, and compare it against algorithms designed for this purpose. We focus on three attributes: the gender of the author of a piece of text, the country in which a set of photos was taken, and the link missing from a social network. For each of these attributes, we find that people's effectiveness is inferior to that of AI, especially when it comes to hiding the attribute in question. Moreover, when people are asked to modify the publicly available information in order to hide these attributes, they are less likely to make high-impact modifications compared to AI. This suggests that people are unable to recognize the aspects of the data that are critical to an inference algorithm. Taken together, our findings highlight the limitations of relying on human intuition to protect privacy in the age of AI, and emphasize the need for algorithmic support to protect private information from attribute inference.