Because switches that don't support VLANs don't know how to forward the VLAN tagged traffic without breaking the tagging. You need the APs to tag the traffic, as only it knows which wifi network a client is on. The router needs to see those tags of you want people on different subnet. All the switches it passes through between the two need to know about VLANS.

Any switches that aren't on the route from AP to router can stay as they are.