You forgot the option, "Enormous sinkhole of time and money that is generally a tremendous pain in the ass".
Seriously though, whether or not it's a right depends on what you mean.
In the sense that I believe that anyone who is financially qualified to buy a home should be able to buy whatever home they can afford regardless of race, religion, age, gender, sexual orientation, marital status & etc... then I guess yes, in a sense, it's a right.
In respect to whether or not everyone is entitled to own a house by simple virtue of the fact that they exist and the implied obligation of society to provide them with that house in the event that they're unable to afford it, no, nobody has that right.
I can also see where home ownership is a privileged to the extent that the means to purchase a home are frequently contingent upon a lender's willingness to lend the money necessary to buy the house.
In a perfect world the only consideration in a lenders calculations as to whether or not a particular individual deserves the privilege of being extended a loan should be the lendee's ability to repay the loan (calculated as a function of cash on hand, income, and credit history).
Given what we know about the mortgage lending industry's use of "redlining" it's clear that credit worthiness is not always the only consideration where lending is concerned.
Since the Fair Housing Act of 1968 makes "redlining" on the basis of race, religion, age, gender, marital status & etc.. (no mention of sexual orientation here) illegal I think that goes back to the point I made above about home ownership being a right (provided the necessary conditions in respect to being able to purchase the asset are met).