So yet something else that was cut out of the final edit of the film was the long awaited explanation to the past between Jack and Beckett. So since we still don't know, here's my theory!
They're half brothers. Same mother, different fathers. Beckett is the eldest. Mother is sailing to somewhere from England and ship is taken by pirates. Jack is the result of that. At some point, Jack and Beckett meet and all is not brotherly love -- it hasn't been said outright, but it has certainly been suggested that Beckett is the one that gave Jack the pirate brand. . Perhaps their mother at some point had a chance to come home, but chose to stay with Jack's father (and if I wrote POTC fic, that would be a story I'd love to write!).
There you have it!
That tasted really good!