Do guys have to double text girls these days?

I came across a thread on Twitter where a girl said she forgets to text her SO and he double texts her when he needs to, so guys shouldn't be afraid to double text in general. Someone also said it was basically being too prideful as a man if you don't double text.

I don't double text as a rule of thumb. For example, I didn't double text this one girl after she stopped texting me (she was studying abroad, she said she was super busy at one point). The thinking was, "she's busy now, she'll get back to me at some point" since we had known each other for a while and had good chemistry in person, but she didn't so I left it alone. In my mind, if she's really interested, she won't just forget about me altogether. But seeing that thread has made me question what happened with that girl (plus I have a buddy who has gotten back to work and isn't texting back nearly as much, it makes me think she was being genuine).

Am I right to have this rule, or is double texting normal now?