Although I really wish I was small enough to get away without wearing a bra - the truth of the matter is, I'm sure I'd seriously knock myself out if I didn't
I do think there is something in the idea that bras restrict the lymphatic system but I also agree that deodorants also have something to do with an increase in disease - along with diet, pollution etc.
In all honesty - there are probably too many variables to be able to blame just one thing so I prefer to reduce the risk as much as possible by eating healthily, using chemical free deodorants/shampoos/soaps and taking regular exercise. Going braless a little more often is certainly an option indoors but I've got to be practical too!
Ironically, on the 'taking regular exercise' point - I was reading earlier today that chlorine causes asthma. My favourite past time of swimming a mile every morning could then be considered a risk - but weighing it up - is no exercise better than risking asthma through chlorine inhalation...when no exercise could contribute to asthma anyway? My point is, whatever you do - there'll be someone out there telling you it's dangerous to your health!
Make informed decisions and you probaby won't go far wrong.