A beginner question: Why we need to assign IP addresses on LAN if switches are not able to read them? Because of ARP (Address Resolution Protocol)? But Switches can't send ARP requests (switches can't read ipv ), right? Who sends the ARP request then?
If i read your question as "why do I have to assign IP addresses to my clients" the answer is: You don't have to. There are other protocols then IP (I guess you mean IPv4 because you are mentioning ARP). You can use IPv6, IPX, Appletalk, ...
You need some protocol on Layer-3 (like IPv4, IPv6, IPX, ...) so that your hosts can talk to each other and to other parts of the network.
As mentioned by others: On a Layer-2 switch IPv4 is only used for management. A pure Layer-2 switch should not care about protocols above layer-2 for switching packets.
As a side note: There where / are some older chips used in switches which can't do Ethernet multicast and can't be used in (most) IPv6 environments.