This is a bit of a catch-22 - to get permissions to raise issues, you need to contact Atlassian, but to contact Atlassian, you mostly need to raise an issue.
However, you've not said where you are trying to create issues.
Atlassian have a lot of projects and my understanding is that there are at least two Jiras behind the projects.
One Jira is relatively public - you can browse a lot of it without a login, then sign up, and you'll be able to raise bugs and improvements for them to look at. You don't have to be a paid user, it's a generalised public forum, like Answers.
The other one is the support Jira. You can only raise issues there if you have an account that has a licence for one of the products (and you're limited to that product). If this is the one you need access to, then you need to use an ID that has a licence associated with it - go to my.atlassian.com and check that.
I have an issue where I'm logged in and looking at this issue: https://jira.atlassian.com/browse/CONF-31867 which is exactly what I'd like to see improved, but I am unable to add a comment. I can see other people's comments, but I have no way to add my own. I'm able to watch and vote on it, but just not add a comment. Any ideas anyone?
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