My (35M) gf (30f) thinks I should sell my house in order to make it fair for us to move in together

My (35M) girlfriend (30f) thinks I should sell my house and rent or buy together to make it fair

So, context.

I own my own home. She rents. I’m interested in her moving in, but she’s only interested in living together if she owns something or I have to “go through the same thing she goes through if we split up” meaning we both would be looking for new places to stay if we split.

I told her it’s not fair for me to have to sell my home in order to live! together, and finding another place to rent is far easier than buying another home if we split up. She disagrees.

She thinks both of us “starting fresh” is the only way to make it fair. I’d like to get opinions

She is right? Is it unreasonable to make me sell my house just to rent together? I’d never own a house together with just a girlfriend who could split at any time. Opinions?

Update: After some conversation, she still doesn’t get it or understand other peoples point of view on the subject. She says I’m being self centered. I’ve broke up with her, the gas lighting and blatant manipulation is just extreme.

Thanks for all the messages and opinions, I’ll respond to some when I can.