Personally, I find the veto to be extremely controlling and indicative of insecurities.
How would you feel if you started to have feelings for a man or woman and HE told you, nope, you can't see him/her cuz I just don't like the person?
If it's just a bad feeling, that doesn't seem like enough of a reason to make him get rid of her. I'm sensing, based on what you've said, that it's because this is the first woman to attach herself to him, without connecting to you.
What is it you're making them wait for...?