Your family is just worried about you being a "starving artist". They don't want to see you living in squallor trying to get by, asking people for money and not being able to pay them back, and ultimately, unhappy because of this. What needs to happen, is you, or they, need to do some research into the film industry and start to understand what kinds of jobs are out there. Help them understand that you can get a job and support yourself rather well.
My parents and I went through this process when I decided to go study at an art school for illustration. Once they researched what kinds of jobs I could get and exactly how widespread the field really is, they relaxed about it because they realised I could make a living off of this.
They're just worried that if you aren't successful, then they will feel like they failed somewhere as parents. Because that is a big part of their job: To raise you into an independent adult that can take care of itself.