M(37) and fiancee F(27) Buying a house as an unmarried couple - Advice please

I had initially posted on the r/personalfinance and was advised to repost here.

The situation is fairly straightforward:

I'm M(37) and my fiancee is F(27). Been together for 4 years. Engaged for less than 6 months.

Seen a nice house, want to make the purchase. Offer is accepted. Present situation is we live together in an apartment.

Fiancee doesn't have the financial ability right now to contribute towards a downpayment or shopping for the house because of student loans.

Fiancee wants to be included in the title so that she "feels like she owns the home". Remember, she has no legal financial obligations to the mortgage note because I'm paying for everything, downpayment, closing costs and shopping for furniture etc.

I propose we see a lawyer to sign a cohabitation agreement to ensure that when she is done paying for her student loans and is in a better financial position, I can add her to the title when she brings her contribution to the table. I gave her no time limit on this and her contribution is just 1/3 of the overall downpayment and shopping expenses.

She doesn't want to see a lawyer and says that our relationship should be based on trust and that I should take her word for it that when she gets in a financially better position, she will pay me for her portion of the downpayment and other associated expenses.

She says that she feels like the only reason I want to go to a lawyer is because she is not contributing any money towards the house.

She also says that I want to go to a lawyer because I feel like she might screw me over in the future and that that's not the type of person she is. She is lovely and I know she isn't that type of person but that doesn't mean we shouldn't have a legal document that stipulates what happens if we break up, what happens when one of us dies e.t.c.

She also says that a certain person said that if you go into a relationship thinking that you will break up, that negative thought becomes a reality. I was baffled by this and really need feedback on this. We don't get car insurance because we think we will have an accident. We get it to protect ourselves from liabilities of a potential accident. Isn't that a very simple thing to understand?

At the moment, to enable her to accelerate her student loan payments, I've taken over a good chunk of our bills. I pay rent, holidays, all utility bills, car insurance for the both of us and even for the most part, I pay for any of dinners or concerts or entertainment. Her only financial responsibility is food and any of her personal bills e.g. salon, cell phone, her gas or her medical expenses (we both have health insurance through our employers).

I have offered her the option where I buy the house on my own as I can afford it and we keep the status quo (mentioned above in point 8) and then we can both save money to buy "our home" when she is ready. Basically the only different is the rent payment will be a mortgage payment and nothing else.

She has constantly complained about how small the apartment we live in is and that was the motivation to buy a home.

She also said that if I had told her about contributing to the house, she would have stopped paying her student loans and saved with me for the house. I disagree with this because I basically wanted her to reach financial freedom faster when I took over most major bills.

I'm I being unreasonable here? I've tried over and over to make her see my perspective but she doesn't want to see a lawyer and the relationship is on the verge of collapse because of this.

TL;DR fiancee wants to be put on the home title (with no financial contribution towards the home purchase) but doesn't want to see a lawyer about creating a cohabitation agreement