Facebook Ads Manager – Why Instagram Videos Can’t Create Custom Audience

You are doing it right. When you login account using Facebook it synchronize your account with Facebook by using details from Facebook and didn't ask for password. But when you are deleting account they want you to login it separately and then delete.

From the Instagram Help Center page, To delete your account:

• Leave the Instagram app and log into instagram.com from a computer. You cannot delete it from your mobile application.
• Click your username in the top right and then select Edit Profile.
• Click I'd like to delete my account in the bottom right.

For security reasons, we can't delete an account for you. You’ll need to be able to log into your account to delete it. If you can't remember your password or username, see some tips for logging in.

Below is an excerpt from Instagram's privacy policy as it stood at the time this question was posted. The full policy can be found at https://www.instagram.com/legal/privacy/

Beginning of Instagram Privacy Policy excerpt

In September 2012, we announced that Instagram had been acquired by Facebook. We knew that by teaming up with Facebook, we could build a better Instagram for you. Since then, we've been collaborating with Facebook's team on ways to do just that. As part of our new collaboration, we've learned that by being able to share insights and information with each other, we can build better experiences for our users. [...]

• [...]When you use our Service, our servers automatically record certain log file information, including your web request, Internet Protocol ("IP") address, browser type, referring / exit pages and URLs, number of clicks and how you interact with links on the Service, domain names, landing pages, pages viewed, and other such information. [...]
• Log file information is automatically reported by your browser each time you make a request to access (i.e., visit) a web page or app. It can also be provided when the content of the webpage or app is downloaded to your browser or device.
• When you use a mobile device like a tablet or phone to access our Service, we may access, collect, monitor, store on your device, and/or remotely store one or more "device identifiers." Device identifiers are small data files or similar data structures stored on or associated with your mobile device, which uniquely identify your mobile device. A device identifier may be data stored in connection with the device hardware, data stored in connection with the device's operating system or other software, or data sent to the device by Instagram.
• A device identifier may deliver information to us or to a third party partner about how you browse and use the Service and may help us or others provide reports or personalized content and ads. [...]
• [..] We may share User Content and your information (including but not limited to, information from cookies, log files, device identifiers, location data, and usage data) with businesses that are legally part of the same group of companies that Instagram is part of, or that become part of that group ("Affiliates"). Affiliates may use this information to help provide, understand, and improve the Service (including by providing analytics) and Affiliates' own services (including by providing you with better and more relevant experiences). But these Affiliates will honor the choices you make about who can see your photos.

End of Instagram Privacy Policy excerpt

Essentially this means that Facebook and Instagram have ways of determining that you are the owner of both your Instagram account and your Facebook account and they don't need to rely on your email address being the same for both accounts.

By signing up for Instagram you gave consent for them to collect your IP address and any device identifiers and to share this information with Facebook because they are the same group of companies. Facebook and Instagram may have more ways to establish a link between your accounts but this explains why they have linked your accounts without using your email. You could attempt to only access a new Instagram account with a different device and from a different Internet connection but without knowing exactly how the accounts have been linked there is no way to know if that will work.