atextia 

inability to send, read or understand text messages.

He claims that he has good knowledge of texting but he is actually suffering from atextia.

atextia by uttam maharjan December 30, 2012

war of atextion

A war of attrition, via text:
When two people are texting each other, usually from late evening to the wee hours of the morning. The victor is the person to have sent the last text, the loser having succumbed to exhaustion and failed to respond.

1. "I thought I pwnd that war of atextion, but when I woke up I had one new message."

war of atextion by iSlur February 19, 2009

atextual 

A person who does not communicate via text message or is unable to because of lack of technical prowess

"Oh you sent Chinatown larry a text. He is completely atextual and can't work his phone and would be more comfortable using pigeons to communicate

atextual by shim1 November 11, 2015

atextual 

a person who doesn't like to text using their cell phone

Joy doesn't like to text using her cell phone. She's atextual.

atextual by BriteWorld November 2, 2010