Thanks for reaching out to Jotform Support. Unfortunately, our German Support agents are busy helping other Jotform users at the moment. I'll try to help you in English using Google Translate, but you can reply in whichever language you feel comfortable using. Or, if you'd rather have support in German, let us know and we can have them do that. But, keep in mind that you'd have to wait until they're available again.
Now, coming back to your question. If your form is set to Private, anyone who uses the form will be asked to sign in/up. That's because only someone with permission from you can access your Private forms. This means that we need to change your Form Status from Private to Public. It's easy, let's do it:
In Form Builder, click the Publish tab at the top of the page and open the Quick Share section.
Click on Private Form and then select Public Form.
Now, anyone using your form won't be asked to create a Jotform account when filling out your form.
Give it a try and let us know if you have any other questions.