In our case a few reasons.
Firstly, the local state schools, primary and secondary are very good (rated outstanding) and in terms of location were well placed for doing the school run at primary or bus service at secondary (allowing DH and I still get get to work on time).
The primary also had a great (and not exorbitantly priced) after school club associated with it, lots of activities, after school snacks (fruit, crumpets etc) that again alleviated the pressure for two working parents.
The four or so private schools within a reasonable travel distance were still a PITA to get to. Travel time for the children would have been 45 mins each way minimum.
After school/breakfast clubs were provided but very expensive. We could have covered it but it was just another issue "against" this option.
These schools also took boarders so all children went to school on a Saturday morning - even day pupils. Frankly we rather like the children and enjoy doing things together at the weekend
. Tbh this was probably the biggest deal breaker for us. We'd also heard (admittedly anecdotally) that there could be friction between the day pupils/boarders.
The private school were all good (facilities/reputation/results) and I'm sure the children would have done well there. I'm not bashing private schools in the slightest.
However, we were lucky that the state option was so good and ultimately far more accessible to us overall. The kids have thrived there and I've no regrets.
Ultimately it's meant more financial security for us as the income that would have gone in fees has paid off the mortgage early. That said, had the state option not been as good we would have paid the money and gone private.