I agree, that is something I never expected! To become so used to having a bra on that I do not feel right without one on.
Once I got up the courage to wear a bra to support the "guests/ girls" I used the tightest sports bras I could to hide everything. In time the ache from squashing the "twins" just was not worth it. Save the hurt and bother, get a good quality bra which is a simple support device. If it was called an "ordinance re-organizer" we would have no qualms about it...probably, but we have attached female significance to an article of support that should be for both sexes since we both need it.
Finally, speaking of attachment and getting accustomed to something: I cannot do anything without a bra on now days. I sleep in one, work in one around the house, go to grad school in one, and go to work in one. Life has evolved to the point where I relax around the house in a bra and never have the "twins" out on their own, except for the requisite shower. You had to get used to wearing socks and shoes. So what is the difference aside from cultural expectations that are ill-founded.
A small side note: I was absolutely paranoid about my breasts and did everything to crush, squash and hide them regardless of the hurt it caused me (duct tape leaves scars). I was ashamed of what was happening and terrified that someone would find out at work. I thought I had a set of mountain ranges on my chest for all the universe to notice. Wrong!!! Aside from the fact I am a large 44 A and headed for a B, people do not notice. I have been asked if I am working out because they see my enlarged chest and figure that is the cause. I did have a female co-worker find out when I had to adjust a bra strap and she started giving me advice on different bras that I might want to try. Turns out her brother has had Gynecomastia since his teens. She suggested I get a bra fitting. People really care if they are given a chance, so do not worry about a bra. Get a good quality one that feels good with your "twins" and relax! You are in great company and we are your brothers. Now, go get your better half and take her out for an ice-cream cone. Life is good!!