How to solve the issue that a Mac (Macbook Air) keeps on trying to use WEP to connect to Wifi?

Solution 1:

I set the Linksys (Cisco) router so that all the 2.4GHz and 5GHz support essentially the same thing: WPA Personal and it seems to work fine now.

I think the issue was 2.4GHz and 5GHz was set to WEP and WPA, respectively, due to some 2.4GHz device using different security standard. So I think the Mac might have some issue of not able to remember the connection, being confused by difference in settings of 2.4GHz and 5GHz.