I was in the same position as you many years ago. My parents encouraged me to pursue a university degree after I completed HSC, which I did. Whilst at uni, I worked the graveyard shift at a servo and used that income to pay for my PPL. After uni, worked as a school teacher (one of the most dangerous jobs I've had) and paid for my CPL and MECIR and instructor rating. I was teaching for a good 10 years before I got my first job as a pilot. Mates of mine who I finished school with, took flying lessons as soon as they finished their HSC. One is now a 737 check and training captain at QF Domestic, another a management captain at JQ.
I now fly an RPT turboprop for an airline in South East Asia and my parents fully support my decision to change careers some ten years ago. I guess parents just want to ensure that their children have a good stable future, and the traditional pathway to an airline career via GA has never been that. But with a degree and work experience in another industry, you can always go back to your other qualification if things don't work out on your way to an airline career. I've personally had to go back to relief teaching more than once, in between flying jobs due to things not working out in GA for me and for this, I thank my parents for encouraging me to pursue a degree earlier on in life.