Adding tags requires that you have permission to edit the question, or have the 'retag' permission. The people who have permission are the owner, and those with high enough karma https://answers.atlassian.com/faq/#edit
From the same page at https://answers.atlassian.com/faq/#karma you can see that you need 400 karma points in order to edit another persons question, but only need 150 karma points to retag.
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