I have been on the other side of this fence. I am a parent whose 'child' changed their major. There are some very good answers here; I'll add what I can.
First, this is recent and a shock. Give it some time; your parents are possibly grieving the loss of the future they envisioned for you (and themselves; futures tend to be intertwined in the mind), regardless of whether they do or don't have a right to have such a vision. Give them the benefit of the doubt - for now - that they have your best interests at heart: the ability to support yourself reasonably in the future. Try to avoid thinking of it as a lack of love or support. Talk to them calmly about their hopes for nowyou; find out why they're so upset (even if their reasons are ridiculous in your mind.) Serious conversations work better if the parties involved understand one another.
Second, do some research to show them that you're approaching it as a mature decision. Find out whether you can make a living in your chosen major. For example, if you want to be a therapist or neuroscientist (or whatever else you might be thinking about), how much demand is there for the kind of career you want to have? How many additional years (beyond college) will you need to complete to do what you want to do? If you can show your parents that this is well thought out, they will be more likely to respect the decision.
Third, point out the grades you earned in the classes you took. Good grades never hurt.
Finally, this isn't the all-or-nothing end you might feel it to be right now. There are cheaper colleges you can attend, and you don't have to continue your education right now, uninterrupted. That's a kind of bifurcation, when in reality, there are many more options open to you. You just need time to explore them.
My parents could not pay for my college; I ended up taking a year off to earn some money (while living at home) and continued to work during college to pay my own way. Not the ideal student experience, but I did what I wanted to do. I appreciated the room and board while they provided it.
Regarding my son, he changed from a science major to Art. I didn't think it was a great idea at the time, but we loved him and wanted him to be happy, so we supported his decision. (He did not do the research I recommend for you, though, because his major wasn't a deal-breaker for us.) We continued to pay for his education - what wasn't covered by his academic scholarship - and he graduated happy and full of hope. It didn't work out for him, and after several years of not making a living working in his chosen field, he went back to school - on his own dollar - and now is happy, successful, and supporting himself well in a Biology-related field. Go figure.