What is the reason in protocol eigrp after selecting the networks we write (no auto summary ?

because this command turn the protocol from classful into classless routing protocol.

when you enter this command, it send the subnet mask for all networks so you can use it in VLSM networks.

The no auto-summary command prevents automatic route summarization on classful boundaries, which would otherwise result in routing loops in discontiguous networks.

To get the subnet mask.

Here is a page of the EIGRP Commands, it is very detailed and well explained and contains what you need to exactly know.

http://www.cisco.com/en/US/docs/ios/12_2/iproute/command/reference/1rfeigrp.html#wp1017389

Hope this was useful and helpful for you.

protect wrong summaries in discontiguos networks !!

EIGRP automatically summarizes on the major network boundaries by default. . “No auto summary” disables this feature.

If you are using a routing protocol that auto-summarizes (such as RIP or EIGRP) it will send the subnet mask of the classful boundary, and not the actual subnet mask. The command no auto or no auto summary will turn this feature off in RIP and EIGRP, and send the actual subnet mask. If you are using OSPF, you don't have to worry about it because OSPF does not auto-summarize

if you have172.16.200.0/24 and172.16.32.0/24 on different network, auto summary will advertise it as172.16.0.0/16 so there will be communication error for the hosts who are sitting between those two subnets.