Sometimes, you need to sell yourself. What I mean is that you need to sell your services and make sure that people know what they want. If they do, then its great, but even after meeting you, they keep questioning the stuff, you will feel crap about it.
I usually prepare for meetings, I usually seek out infromation about person I am meeting, to make sure that I understand them and set some context around their requirements. But when your client does not do that, he does not even care who you are, then one of the most simple things you can do it walk out with a smile.
But what if your colleagues keep doing that? what if you keep doing same excercise again and again to the question : Prove me that you are worthy? Well at this point of time, its time to stop this stupidity and move on with life.
This has happened with me in my previous organizations and I believe that this will continue happening now as well, while this is crazy as it sounds like, at some point of time you just give up.