No, completely incorrect.
You have “marital interest” in the house. It is half yours regardless of the mortgage. Regardless of the deed.
He cannot kick you out. He would be laughed out of court. You can however leave the house of your own free will and if you do you will not be able to come back.
Do not move out. Do not sign anything. Talk to an attorney.
Leaving does not me runs to the grocery store etc. Leaving means packing up your stuff and moving out. Be careful. If you go to the grocery and he changes the locks and says you moved out there will be problems. You will get back in… eventually.
Conversely the fact that he is on the mortgage and not you is a good thing. If he defaults on the mortgage they will come after him, first. Still may come after you, but they will have a harder time there.
Hope this helps.