Well that's the same in the UK or US tbh afaik. Nobody really gives men much slack w.r.t. anxiety and it will be seen by the majority as weakness.
Ignore brothers /family as much as possible, imo (which is a pretty good piece of advice for you, from what you have posted about your family before). I wouldn't even bother to argue your case, it will just create resistance (you won't change those beliefs). Accept that it isn't weakness and do what you can.
Enough about me, lets talk about you, what do you think about me?