I finally took the time to read the emails from Ryanair, now that they're published in full. The don't seem completely unreasonable (It may be a bit counterproductive to demand apologies from avherald though):
News: The Aviation Herald under legal threat by Ryanair
All this seems blown out of proportion. I don't think safety culture or freedom of press will be seriously harmed if the cited comments are deleted. I don't think said comments contained a lot of valuable and/or new and unique information.
But Ryanair may have contributed to blow this out of proportion, with their legalese and somewhat confrontational emails. I am not a lawyer and I have no idea whether these comments could be construed as defamatory, under whatever law. Fact is, Ryanair does have an excellent safety track record. They could as well just have ignored these comments, if they wanted to avoid drawing attention to them. It's hardly surprising that a media outlet will publish letters sent to them, particularly if the letters may be perceived as threatening. And the more "private and confidential" stamps there are on them, the more likely they will be published. Ryanair could have anticipated that. I don't think there's much for Ryanair to win here.
sometimes legal action to delete allegedly defamatory statements, or otherwise (allegedly) infringing content, has the opposite effect. it just draws further attention to the issue.
I had never heard of untied.com, the "united" critisism site which has been up and running for 15 years, until united/continental filed a lawsuit against the maintainer of the website (a McGill University engineering professor):
United Airlines attacks Untied.com
then again, ryanair hired a "litigation specialist". and now that person probably wants to justify his/her salary.