OP- why did you two move in the first place? Did you move because he got a job in a new location and you followed him? Are you living in the same town but he wanted a better flat and then for some reason you lost your job?
What it sounds like to me is that you both moved into a new flat and you contributed to the move as you said. You are unemployed and still looking but in the meantime he is having to pay the rent and the bulk of the bills. He knows that you have a sizeable saving that you are not willing to put toward the rent at this point because you've already spent a large portion of savings on the move and additional bills. You feel at this point you want to protect what you have left in your savings because it is for a house. He, however, brings home a sizeable income but hasn't chosen to save any of it so the prospect of spending more of his paycheck than what he normally does stresses him out and he's worried that he's going to spend his entire check on bills and living expenses and feels like you should pony up some more savings so he's not having to cover everything.
So you are at a stalemate.
If I understand that correctly then both of you have legitmate concerns. But what you are seeing is how he deals with crisis and life is going to be full of crisis at different points. You need a partner who will be supportive, understanding, and uplifting when times are tough. You both need to be willing to be flexible given the unusual situation. Either of you being stubborn on your position is not going to end well.
You are wise to 'save for a rainy day' because one thing is for sure its going to 'rain' (like losing your job) and if it doesn't you will have a nice nestegg for a house payment or whatever. I know it takes a long time and good discipline to save so well done.
I wonder though..... do you consider that your savings or savings for both of you as a couple? I ask that because if he sees you're not willing to spend anymore from your savings to contribute to the monthly household bills because that is yours then he is asking why is he expected to cover both of your expenses - he sees his money as his.
You might need to seek counseling and get an unbiased third person's opinion especially where you feel you are the only one giving in (90% of the time) and you want your voice to be actually heard. (but someone will have to pay the counselor....)
Perhaps during this time of upheaval due to unemployment you could work a deal where you pay rent every other month so he feels you are still willing to contribute and you're feeling that you won't lose your entire savings.
But, after nine years together you should be able to come up with a workable solution. If the arguments continue then you will need to, as you know, consider ending the relationship. Money issues end a lot of relationships especially after marriage. Maybe you could schedule a meeting with him to calmly discuss the fiancnes when neither of you are mad with the prearranged agreement that both of you need to not be interupted and tempers can't flair and see if you can work out an agreeable solution.
Best of luck to you.