I personally feel like therapists should make exceptions to their cancellation policy if a client is sick (that's what mine does), assuming it's not a frequent occurrence. In this case, if she's telling you she doesn't want you to come in and saying you don't have to pay, I'd probably just take her up on that (but it did sound like she was trying to guilt trip you a bit). Well, I'd probably do a virtual session unless I was so ill I couldn't manage that, which is something I've done recently a couple times (I got used to them during Covid).

Could you maybe try a virtual one? If you really don't want that, I guess pay half then?