Kate Gregory has outlined the answer, but perhaps more detail is necessary for non-native speakers to understand the underlying assumptions.
First, in the Time article the writer is using an extended metaphor sometimes referred to as a "literary conceit":
In literature, a conceit is an extended metaphor with a complex logic that governs a poetic passage or entire poem. By juxtaposing, usurping and manipulating images and ideas in surprising ways, a conceit invites the reader into a more sophisticated understanding of an object of comparison.
The "more sophisticated understanding" we are being invited into is one involving standard, commonplace tropes from romantic breakups.
First, the title refers to the standard plain-truth version for ending a relationship that is usually given by a third-party to the person being jettisoned:
"He [or she] is just not that into you."
In other words, it's over. Get past your issues with the breakup and move on with the rest of your life. In the context of banking, banks are being told by the third party (Time) that consumers really don't care about them anymore.
Here's where Kate's answer enters the picture. The standard trope "It's not you, it's me" — used to absolve the other party in the relationship of blame as a way of pre-empting any desperate attempts to salvage it: "But I can change!", "We can work it out!", and so on. By taking responsibility for the breakup there is no possible comeback. The person on the receiving end of the breakup is left without recourse.
Now, we have to address the fact that this trope is inverted: "It's not me, it's you." That plays the trope for laughs, since instead of absolving the jettisoned party of responsibility, the person broken up with is saddled with all of it. In this case, the banks are being seen by consumers as bearing all the guilt for the relationship falling apart, and are (by refusing to use banking services) being told so by them.
By using such devices, the writer presents the information in a light, clever style that is not strictly suited to the bald representation of boring facts about banking, but which is no doubt much more readable for the same reasons.