Honestly, as someone who is both going through the Big-Co. hiring process myself, while also interviewing cadidates for replacing myself, I'd say it's 50% skill

Honestly, as someone who is both going through the Big-Co. hiring process myself, while also interviewing cadidates for replacing myself, I'd say it's 50% skill and 50% a crapshoot. They are heavily optimized for turning away bad candidates and as a result have a high false negative rate. Don't beat yourself up over that. My advice: don't take your Dad's offer, yet. Move to the valley. Get a job at a random startup, or big-co. Hell, get a job at a random ass company as the role you want. Provide business value for money for a year then keep interviewing. Also, based on your portfolio, If you are willing to move to the bay area, I'd phone screen you this week. We'd get you a visa.