my apple mail app keeps quiting as soon as I start it on my early 2011 MacBook Pro?

The cause is usually a malformed email message.

Press and hold a Shift key while launching the Mail app again. That will launch the Mail app in windowed mode (not full screen) with no message selected. In that manner you may be able to identify the problematic message, and delete it.

If that does not resolve the problem, please refer to If you can’t open Mail on your Mac - Apple Support.

Are you still using OS X 10.11 as indicated in your profile information?

The older a mail client becomes, the less able it will be to cope with more recent email message protocols. You can upgrade that Mac to OS X "High Sierra", which is almost certain to fix what's wrong with Mail.

Start here: How to get old versions of macOS - Apple Support, and scroll down to Use Safari to download macOS on your Mac.

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I believe that if you upgrade to High Sierra (read below), you may be able to squeeze a bit more life out of that ten year old Mac.