Talk to her and find out what it is that she is afraid of - is it the actual pool? If so, what part? The getting in? The getting wet? Does she have to wear a hat? The getting dry again afterwards? Or is it the swimming teacher? The other children? ... the list is endless. Once you have a better idea of what exactly it is that she doesnt like then you can work with the school to over come it.
If she is at a private school that has a pool and is already having lessons then I suspect they will continue to use the pool until they leave meaning you need to nip it in the bud now, as I am sure you can appreciate that she has an amazing opportunity with this set up for which you are already paying. Did your older children go to this school? What happens as they get older? It would be "easier" to duck out if she were at a state school doing 6 weeks of "swimming" each year in a run of the mill council run pool which is a drive away from school etc but that wouldnt actually help your child either, and it is in both the school and your family interests to work together on encouraging her to use the pool at school.
Also try and reframe it - if she were afraid of another element of school life (either a subject, eg English or an aspect eg lunchtime) then how would you approach that? Presumably you wouldnt just say "oh you dont need to do it at school, I can teach you in my own time" or pick her up, take her home, then return her to school each day for lunch? That really wouldnt do her any favours long term, and I dont see how this is any different.
For what it is worth, I had similar with my child when he was about 4. He had always loved swimming and was pretty good. Then he just started crying/was really anxious from the night before, all the morning before school, all the way to the pool, when we got to the pool etc and he screamed when I got him onto the pool side. It would have been so easy to give up and let him "win" but I kept taking him every week as a non negotiable thing, then eventually, after several months he settled again. I never did work out what it was but he loves swimming again now aged 7 and trains twice or three times a week with his swimming club. If I'd have let him win, then realistically, he wouldnt be swimming now as we were at a state school so he would not have started school "swimming" by now.