Just wanted to add my support OP.
I don't often comment on relationship issues because everyone's is different and sometimes my own view is a bit skewed due to my own experiences in controlling relationships, however the alarm bells here were too loud to ignore.
It really seems like you are being set up for being "in the wrong" no matter what you do or say.
If you agree despite your discomfort in order to be "nice" he will wonder how far the "not minding" can be pushed - he can frame further boundary pushing by suggesting female solidarity "Now that you know her / have the bond of being female you must be able to see she's not a threat so it'll be okay if I do x, y or z with her on this day when you're not available..... what harm can it do? She's YOUR friend too" ......
If you say no and sick to your guns, there is the risk he will use it to justify having to sneak around behind your back, tell his pal what a controlling, jealous unreasonable woman you are and then say if an affair develops that he was pushed into it by your refusal to accommodate his "friendship".
Another thing that strikes me here is a possible view of and enjoyment of the idea that he is a worthy prize to be fought over by two women who are both supposed to revere and admire him for his selfless, caring qualities. Maybe she has pursued him - maybe they have had chats which he has cherry picked things from to stroke his own ego - as he has taken your no as a yes, it appears he has a problem with actually hearing and accepting what a woman says because only his wants are important and he constructs his world view to justify them, even if its demonstrably false.
You say he seems desperate for this meet up - is it lockdown fever, or saviour complex, or a clever way to facilitate his desire?
I would love to ask this woman what has happened in their conversations to prompt this and whether she is as invested as he seems to be?
But he is the brick wall between any sort of honest communication in all this between you because he could accuse you of ganging up on him, misinterpreting his genuinely altruistic motives etc etc because "jealous women" "man hating etc etc".
So he's kicked open a hornet's nest and potentially exposed two women to the stings of male manipulation.
Just my thoughts and I really hope this gets resolved with the best outcome for you.