I've been through similar in the past, where I had year's of on-the-job training in the relevant applications (Quark, InDesign, Illustrator, Photoshop, Pagemaker, Freehand, Persuasion, etc.) but wouldn't even get an interview simply because I didn't have a degree (didn't matter what degree...it could have been in washing dishes...but it was a tick box that needed ticking).
Luckily, over the years, I've built up a good network of clients/companies who rate experience & familiarity over qualifications, and want me for 3 month to 3 year projects. When I'm coming towards the end of one project I communicate my availability status to my network. Most I have off between projects is about a month, and that gives me time to have a break to go on holiday.
My last 'interview' was 5 years ago, and the client simply phoned me after a recommendation from another client and asked if I could do everything that he'd been told I could. I told him I could, and if he wanted assurances, then I'd come in and work for him and if he didn't like what I was doing I wouldn't charge him anything. I'm still there now, but doing a slightly different role than I started (less design, more project management)!
Most design jobs will require you to be able to read or listen to a brief and then go away and work on it. They're expecting something back that conforms to that brief.
Unfortunately, as you've shown in your replies, you can't even understand why they're asking for specific role requirements, so why would they even consider your application when they'll just expect you to be equally as belligerent on the job?