Her name will be the only one on the mortgage. This means if she decides one day to kick you out, you leave with nothing. All money you put into paying for the mortgage is hers. Just like renting an apartment. She wont owe you anything. Also, if you end up marrying her, the records will show that she bought the home when she was a single, unmarried woman. You also likely get nothing in a divorce situation due to this. It sounds like either her parents got into her head, or she doesnt have a lot of trust in the longevity of your relationship.

Ultimately, I understand her side tho. Shes protecting her investment. But for you, she really isnt looking out for your best interests. But it seems like you are doing ok anyway with your salary and savings. I dont know how long you've been together. If its only been a few months, this arrangement makes a lot of sense. Have you discussed vice versa with her? The possibility of you buying a home and her being the renter instead? If shes immediately unwilling to be on the other end of it, that should tell you something.