Beth and Jaime just had sibling rivalry fueled by their dad.
I re-watched seasons 1 & 2 and first, and first let me tell you that season 3 is going in a new direction and this show will vaguely resemble anything from the first two seasons.
MY OPINION
Jaime and Beth are close in age, definitely in High School at the same time.
Don't be fooled by Beth, she too lives for her father's approval.
I believe Jaime does blame her for their mother's death, something which way older brother Lee would not, and way little brother Kacey would not
and Beth feels that hatred so she just throws it back at him.
Remember conversations from Beth to Jaime in the first season was, your becoming what he wants you to be and he doesn't love you for it.
Taylor's going to have to create more of a back story if h wants me to believe that Jaime had her sterilized.
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Don't get me wrong.
Big fan of the show but this discovery is a big sigh for me.