Why does current flow the opposite way from the electrons?

Up and down are opposites on the other side of the world too...

Anytime electrochemistry is involved it's important. But regular electronics not very much. I think positive and negative mostly trips up people trying to use what they think is happening to explain theory. When it's not that useful most of the time.

What I could never keep straight is anode and cathode.

Actually both wires are full of angry pixies, it's just that you have angry pixies in your body that match the ones in one of the wires, so you don't notice when you touch one, and strongly notice when you touch the other.

On top of that if we did not ground one side of the electrical network, you could touch either wire and feel nothing. That's called an isolated ground, and is not commonly used except in hospitals and some other specialty settings.

(If you wonder, we ground one side because if two different people both happened to touch a wire, current would flow between them using the each.)

It really seems like had a rationale:

"We suppose as aforesaid, That Electrical Fire is a common Element, of which every one of the three Persons abovementioned has his equal Share before any Operation is begun with the Tube. A who stands on Wax, and rubs the Tube, collects the Electrical Fire from himself into the Glass; and his Communication with the common Stock being cut off by the Wax, his Body is not again immediately supply’d. B, who stands upon Wax likewise, passing his Knuckle along near the Tube, receives the Fire which was collected by the Glass from A; and his Communication with the common Stock being likewise cutt off, he retains the additional Quantity received. to C, standing on the Floor, both appear to be electrised; for he having only the middle Quantity of Electrical Fire receives a Spark on approaching B, who has an over-quantity, but gives one to A, who has an under-quantity. If A and B touch each other, the Spark between them is stronger, because the Difference between them is greater. After such Touch, there is no Spark between either of them and C; because the Electrical Fire in all is reduced to the original Equality. If they touch while Electrising, the Equality is never destroyed, the Fire only circulating. Hence have arisen some new Terms among us. We say B (and other Bodies alike circumstanced) are electrised positively; A negatively: Or rather B is electrised plus and A minus. And we daily in our Experiments electrise Bodies plus or minus as we think proper. These Terms we may use till your Philosophers give us better. To electrise plus or minus, no more needs to be known than this; that the Parts of the Tube or Sphere, that are rub’d, do, in the Instant of the Friction, attract the Electrical Fire, and therefore take it from the Thing rubbing: the same Parts immediately, as the Friction upon them ceases, are disposed to give the Fire they have received, to any Body that has less. Thus you may circulate it, as Mr. Watson has shewn; You may also accumulate or subtract it upon, or from any Body, as you connect it with the Rubber or with the Receiver; the Communication with the common Stock being cut off."

from Benjamin Franklin's letter to Peter Collison, May 25, 1747.

Exactly this!

Even the use of 'flow' is misleading. It's barely trickling through the wire...