Please please read the responses from Yoshi P.. This is not a user issue (though can be). 2002 is given when connection is lost while attempting access to login server. This doth not matter if you lost connection or Square servers become overloaded.
"In order to prevent a major login server outage, FFXIV has a limit of "no more than 17,000 total players waiting to log in per logical data center". This cap is set uniformly regardless of how many Worlds exist in a logical data center."
・ The Issue
"If the total number of players waiting in the logical data center exceeds 17,000, Error 2002 will be displayed and you will not be able to queue for login."
Other post;
As we mentioned in our previous announcement (https://sqex.to/eUgyp), there are two causes of Error 2002.
"Occurrence of Error 2002 When the No. of Players Waiting in the Queue per Logical Data Centre Exceeds 17,000"
and
"Error 2002 Occurrence From Issues With the Player's Internet Connection"
I am not defending Square for 2002 but really seriously, this is getting most silly. It is incredibly common when submitting any bug reports to be asked to eliminate any issue on the user end. This makes the process of diagnosis easier. It is not done to be rude.
If swapping routers and disabling anti virus appears to have worked for you it is highly likely you may have been experiencing issues on your end. Tis also most likely you will encounter 2002 again in future as this issue is not user exclusive.
In fact, lobby server issues are quite common for reasons most varied. I have had personal experience with such things when working on emulator software. I have explained many times on the forums about this.. and so wish these threads would remain on topic as they are amusing to read. If and this is biiiiiiig if Square reads anything here, technical dumps will be far more useful for them then passive aggressive insult slinging.
TL;DR
This is server side and can be client side issue. That is all. This has been stated by Square and from my own personal experience seems correct.