Sounds like they didn't like you much at Horizon.
Mesa is a second chance airline, apply there.

"Now, the reason for this was because my captain/instructor told me to NOT put in a transition on the STAR due to the SID having many of the same waypoints."

I'm not sure what on earth is going on here? That to me sounds like a fundamental lack of understanding how SIDs and STARs and the FMS works. Maybe it was a legit fault after all?