but I'm from a traditional background where the husband ( my father) takes care and pays for his wife as the main breadwinner
YABVU with this ^
I think the rest of it has all sorts of "it depends" about it, and none of the answers are right or wrong, just different opinions, which you need to talk about seriously.
You say you are traditional, and yet, you are living with someone, without getting married, and without forming a partnership.
Which is fine as long as that is what you both want.
But, as you both get older, what are both of your feelings on supporting each other through thick and thin. What about if one of you wants to retire early ? Or go part time ? How are your assets split when one of you dies ? Or if you separate ? (Get complicated if he has been paying half the mortgage for years).
Wanting to live beyond your means only works if you are in a place where you both have savings / income other than salary.
In terms of how you split the day to day expenses, sometimes the decision on if it is 50:50 or if it is in proportion to your income, becomes much more important if you are living hand to mouth, or on a tight budget. If you are both on relatively good money, then discrepancies might not matter so much.
However, If I'd been with someone 13 years, 7 of which I'd been living with them, I would like to think that if they did have a lot of savings, they would treat me to a holiday. Of course, difficult to know, if this is a reasonable holiday or a really expensive one, and if you don't have money because you are in a job that pays poorly or if it is because you are a bit of a spendthrift.
So much of this is "it depends" for me.