Let's start by taking a look at the A Mixolydian Mode.
A Mixolydian contains the notes A B C# D E F# G A. A Major contains the notes A B C# D E F# G# A. The only difference is the G. We use the flat 7 because the chord A13 contains the note G. Now you might say, “why don’t we use E Dorian?” Well let's take a look at that scale.
Well, E Dorian has the same notes as D major - D E F# G A B C# D. Let's look at the D major scale.