How do I win over a girl that doesn't want to offer security?

Bro, I understand your insecurity because I've been there... just take it slow and don't be rushed. if things are going to happen, let them happen naturally - don't force something. girls need time to warm up to you and their minds are pretty changeable... you want a girl who is going to be consistent and stable, but stability takes a long time to establish. give her her space and just spend some casual time around her without making her feel pressured into anything.

another thing you might consider: you want to be in a relationship with her, but she won't offer you security... why? has she been screwed over recently and now needs some space? does she not see any potential in you as a boyfriend?

give her every reason to trust you and be completely up-front and honest with her. be transparent and don't play games with her. just be yourself. you want a girl who likes you for who you are and respects you for who you are... if for some reason she doesn't, then you don't need to be wasting your time with her.

This girl is confusing! Unfortunately it sounds like she isn't interested in dating you (don't take it personally). This is probably just her way of letting you down easy. By the way. Does she even know what she meant when she said security? When you say that, (to me) it sounds like she thinks you want her to take care of you financially. Ex: house, bills, car, phone etc.

AH well there are plenty of fish in the sea. Good luck!