Women are strange creatures. As others have said, it's probably about feeling insecure.
My wife told me that if I decided to keep my old place and rent it out after moving in with her, she would have seen it as me keeping a back door open.
As Affieplaas said, getting married with accrual means that as the debt of the house is paid off, she will automatically "get" half of it.
COP is just bad. I am not an expert in the details, but under it both are responsible for the bad financial decisions of the other. You go bankrupt? She goes bankrupt with you.
You take out a R500K loan to help family then lose your job, she gets angry and divorces you? Now she is legally liable to repay that loan as much as you are.
Something happens where you drive drunk, knocks someone over and gets sued for damages? She is on the hook to pay those damages as much as you are.
ANC with accrual just means that you can't get married, and then 6 months later divorce (which happens) and get half of the other one's stuff. You go into a marriage with the best of intentions, but things go wrong. Just because you will live together beforehand doesn't mean that things can't go pear shaped very very quickly after getting married.