C D E F G A BIn any key, the 1st, 4th, and 5th notes become major chords, and the 2nd, 3rd, and 6th notes become minor chords. Let's take a closer look at that 2nd note, D. We know it turns into a D minor chord, which consists of the notes D, F, and A. Hold that thought and let's skip to the notes in the key of D:
D E F# G A B C#As you can see, the 6th note in that key is a B, which happens to be the 7th note in the key of C. If we tack that 6th note (B) onto a D major chord (D-F#-A) we get a D major 6 chord. But if we're operating in the key of C, we're adding a B note to a D minor (D-F-A) chord. THEREFORE we found ourselves a minor 6 chord, Dm6 (D-F-A-B).
So there you have it, just like that man raised by wolves, a minor 6 chord is desperately trying to be something it's not, grasping at that major 6th interval, fighting the very thing that gave it an identity (the flat 3rd), always the wolf, never quite a man.