Wasn't her request, another player told the DM of her phobia and asked him to not include spiders for her sake.
Then he did what he did. It made her pass out. He thought it was funny and refused to apologize. Nobody who was there is planning on forgiving him.
Given the circumstances which were NOT included in the original post - namely the passing out, then the thinking that was funny - it does sound like he was being a jerk.
However, the general principle remains: Objects of fear are not to be avoided in-game. Doing so would cripple the game, because it's a game about being a hero and confronting the bad and scary. If you're too afraid to even let your character do so in an imaginary, safe for you situation, then it's not the game for you I would have to say.
You may not want amateur therapy, but if it's that much of an issue, you NEED to get professional help before daring to game because you are NOT able to function normally in society as you are. Spiders are part of the real world AND part of any imaginary world that is based on an Earth-like environment, and you WILL encounter them at some point.
The DM should not have described the encounter in such detail, it sounds like. Given her fixation, her imagination would easily have filled in, so it was overkill. And he should have started small - a literal small spider on the ceiling, perhaps, or perhaps merely a drow brooch with the
design of a spider on it found as part of a hoard. And then give her time to get used to it. Unless it was an Underdark campaign, that may have been enough.