AITAH for telling my husband I would not move without my name on the house

I (32F) bought the current starter home at age 22. My husband (33M) moved in about 3 years ago just prior to us getting engaged. I’ve always considered this to be our and now our 15 month old daughter’s home, even though my husband has never financially contributed to the mortgage. We are looking to move to a larger house, not because we intend to have additional children but because my husband wants a “man-cave” as well as a WFH office. He also says he wants a large house to host parties just like his childhood home. I support his need for his own space, and also see this potential move as a way to help our daughter get into a better public school jurisdiction. Yesterday my husband told me that when it comes to signing for the new house it should be only his name on the deed. He believes he could qualify for a first time home buyer and this would save money on closing cost. We would be using the equity in our current home (about $200K)for a down payment, in order to afford the new mortgage. I told him as a woman I need to protect myself and would not move without my name being included on the home. I told him it would be stupid of me to use the equity in the home I’ve lived in for 10 years and to not have my name on the new home. I mentioned that if something were to happen, or if his feelings for me changed one day that I would be left with nothing. He became very upset by me saying this. He said my thinking is flawed and I need to go to a therapist to work on why I think like this. I told him I don’t believe my thought process on this is irrational or flawed and that while I understood that he was offended by my statement, this was a non-negotiable for me.

Additional background: my husband makes the same amount of money as I and he pays the electric bill and half of daycare. He constantly talks about money and saving and has made me cancel subscriptions (like the gym) in the past to save a quick buck. When our daughter needed surgery his first thought was “well how much is this going to cost” while mine was is this surgery needed and safe. He grew up in a very wealthy family and I grew up lower middle class.

So Reddit… am I the AH? —————————————————————————- Update: I want to thank each of you for your advice and confirmation that I am not out of line in my thinking. I will be contacting a lawyer to set up a trust for my daughter. I will also work on having a will and power of attorney completed.

I re-visited the conversation tonight with my husband. He stated that “the problem is that I feel like I need financial protection from him.” He feels that he isn’t “doing his job” as a husband to make me feel secure enough.
I let him know I appreciated his input and know he loves me, but that I would not be essentially handing over $200K. I have told him that we should go to a couples therapist for an outsiders perspective to which he replied that he doesn’t want to talk about finances with a couples therapist, but that I should explore why I feel the need to financially protect myself.

I have told him for the time being we will have to agree to disagree as I will not be moving forward with his plan.