Because when they break up she has nothing and he has her money in the form of equity. Splitting consumption bills is obviously good, but splitting a mortgage where one party gets it all is far less cut and dry.

The person renting (man or woman, if the situation was reversed on gender) has no responsibility for maintenance or liability to the house. If the renter is paying rent, they should also have no responsibility to pay for any house maintenance. Roof needs replacing? Homeowner pays, renter pays nothing. Fridge goes out? Homeowner pays, renter pays nothing. Mail carrier slips on ice and sues? Homeowner need to defend themselves, renter pays nothing. If the renter wants to break up and move to Alaska, renter can do exactly that with 30 days or less notice. Homeowner would need to go through all the trouble of evicting and selling the property to do the same.