In answer to your query about why he didn't get in, it will simply be because they had more applicants than places, and the children offered places all ranked higher than your child in their admissions criteria. There will have possibility been some applicants with EHCPs or some who are looked after children (both are given priority in most schools' admissions criteria), then there will have been children who already have siblings at the school, and another bunch who live closer to the school than you. Most oversubscribed schools, unless super popular to the point where even siblings struggle to get in, cut off on the distance section. So, at a guess, I would assume this is where your child fell short. The LA website will likely tell you the break down of places, and how far away from the school the last child admitted lives. In many cases, it can't be less than a mile.
This is an example from one school in my LA, lifted from our LA website:-
Places were allocated to: Fewer than 5 pupils in public care or with an Education, Health and Care Plan; 30 siblings; 18 pupils who live closer to the school than any other school; and 11 out of 18 other pupils using the distance tiebreaker. The last pupil to be allocated a place in the ‘others’ criterion lives 0.918 miles from the school.
In that example, 7 more people listed the school as a preference than they have spaces for. Those 7 missed out because they live further from the school than the other children who didn't meet the higher criterias of having an EHCP, being in care, having a sibling already at the school or living closer to this school than any other school. They will all go on the waiting list, ranked in order according to the admissions criteria (so currently the closest of those children to miss out will be first on the list, but they could be bumped down if other people move into the area to an address even closer to the school, or if a child moving into the area has a sibling who is admitted to an older year group in the school etc).