One reason for asymmetrical error bars is because they actually are asymmetrical. If you enter separate up and down error values, they may not be the same. If you plot median with quartiles, the error bars are likely to be asymmetrical.

But if you plot mean and SD (or SEM), how can the error bars appear asymmetrical. The figure below demonstrates.

The error bars on the bar on the right seem asymmetrical. But look closer. The outer border denotes the mean, and the entire bar’s thickness is inside the bar (for Prism 7 and later). Thus, the error bar is symmetrical around the outer edge of the bar. But because part of the down-pointing error bar is covered by the bar’s thick inner border, the error bars appear asymmetrical. The workaround, of course, is to make the bar borders thinner.