Another reason is that if you're using an image as a link, the alt text for that image will be treated similarly to the anchor text of a text link. However, we don't recommend using too many images for links in your site's navigation when text links could serve the same purpose. Lastly, optimizing your image filenames and alt text makes it easier for image search projects like Google Image Search to better understand your images.
As I had a teacher at school who was always really picky on how to draw conclusions I must say that the conclusions you drew for your health situation might be true, but dangerous. For example: If slightly more women than men suffer from health deseases it could be wise to write the information toward women. But, if you take search behaviour into account thing could look a lot different: It might turn up that men search more than women or that (senior) men are more present on the net than women.
Another example when the “nofollow" attribute can come handy are widget links. If you are using a third party's widget to enrich the experience of your site and engage users, check if it contains any links that you did not intend to place on your site along with the widget. Some widgets may add links to your site which are not your editorial choice and contain anchor text that you as a webmaster may not control. If removing such unwanted links from the widget is not possible, you can always disable them with “nofollow" attribute. If you create a widget for functionality or content that you provide, make sure to include the nofollow on links in the default code snippet.