This article applies to eM Client 9 and newer.

With the introduction of Avatars in the message list the behavior of marking message as read/unread and assigning a flag has changed. 

At first, you see the unread orange dot as usual:

But if you hover, the Flag option shows up instead so you can easily flag the message in one click.

The flagged/unread message then looks like this:

So that means you can easily add or remove the flag in a single click, but this functionality is not available for switching the unread state of the message to read and vice versa.
Once the message is marked as read, you cannot set it back via the message list icons - only through the mark options via right-click, toolbar button or the keyboard shortcuts (Ctrl+Q for Read, Ctrl+U for Unread).

Many cons and pros of having both buttons available and clickable were considered, but in the end, a design decision was reached - the unread dot does not look good when it is not centered with the avatar (and only one icon is shown at the top).
When trying to display the unread dot and flag only on hover (same way as in eM Client 8) it causes the icons to change positions and may lead users to click the wrong icon by accident. This is why we decided to show only one centered icon in this situation.

You can also enable the option to "Always show "read" and "Flagged" icons on mouse hover" in Menu > Settings > Mail > Read under the Message List settings.

If you would like to avoid this completely you can return to the same setup as in eM Client 8 if you disable the Avatars in the message list. 
Simply right-click the top of the message list and open Columns configuration. 
Select the Avatar from the "Show these columns" list on the right and then click the Remove button, which will move it to the list on the left, "Available columns".