They are deductible by another means (business expense). But you pay rent in after tax dollars. Imagine having a neighbor with and identical house--you both agree to swap and rent to each other. You would be worse off than sticking with your mortgage (if you rent to each other for $0, it works out the same as the homeowner deduction).
Not usually true. Investment properties are not subject to mortgage interest tax deductions. http://en.wikipedia.org/wiki/Home_mortgage_interest_deductio...