Why can i not make an avatar?

[echinopsis .]

You can use a photo avatar or a cartoon avatar from another site, and if you have a Facebook or Twitter account, you can also use those avatars.

Go to: http://profile.yahoo.com/y/settings/privacy/ - make sure your profile isn't hidden, because if it is, your avatar won't show.

In case you want to use a Facebook or Twitter avatar, you need to link those accounts in the Profile options.
http://profile.yahoo.com/y/settings/linked-accounts/

You have several options in case you want a photo avatar:
a) go to your Yahoo! Answers settings at http://answers.yahoo.com/my-activity/edit/about , click "Update photo or avatar",
b) go to your Yahoo! Profile at http://profile.yahoo.com/ , click on the current avatar.
Now upload a picture or choose one of the pics you've uploaded previously.

Note 1: if you are on a mobile, you need to switch to desktop mode first in order for this to work.

Note 2: Yahoo no longer supports the creation of their cartoon avatars - it may still work for a few users, but the support was said to stop April 1. And no, this is no joke, the matter was announced quite a while ago...