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From: "new"

The cable guy pointed out that I had about 5.5 amps of current going through
the grounding rod outside my home.

Wondering if this was connected to the flickering light problem I had I
called the electric company (who I must say got right on it in 3 hours).

The wires from the pole coming to the house were rubbing against the tree in
the front yard. The neutral from the pole was virtually cut.

Hopefully, they replaced this "neutral from the pole" as it's usually also the
guy wire supporting the 2 hots.

The current in my ground wire as I understand it resulted from the current
going through either of the two hot legs of the 220 to the neutral in the
circuit box that is attached to the neutral coming in from the pole. As
this was cut, the current instead flowed to the ground rod outside (the box
is also grounded to the plumbing system).

My question is: I guess neutral and ground are joined on the neutral bar in
the circuit box. Why goes not the current always flow to ground? WHat am
I forgetting from my ancient BSEE degree?

What you are forgetting is that ground is for safety, in this case a redundant
backup in the event something just like this happens.

You're also forgetting, utilities don't deal with "neutrals" in the sense that
inside wiremen do - for a utility system there is no "neutral," they call that
conductor just ground. It only becomes a neutral after it has joined with your
ground rod in your main panel.

The current doesn't normally just go to ground (from your panel's neutral buss
bar to your grounding rod and/or water main) because it's easier, and usually a
shorter trip, to get back to exactly where it came from (the utility's
transformer, where their "neutral," - the center tap) via the guy wire. That's
supposed to be the path of least resistance. Without it, all of your home's
unbalanced load would have to flow through your ground rod, into the ground and
make either a b-line toward the transformer's ground rod (If it's present and
maintained) or, to the next home's ground rod, into their panel's neutral buss
and back through their intact guy wire.

Or then again, since you can't tell which way the AC is flowing on your 5.5 amp
reading, perhaps it's your neighbor who has a bad neutral...

Also does this mean when I was checking the ground wire of the cable system
(were it is lugged to the ground wire on the way to the ground rod) could I
have fried myself?

You could have, if that was the path taken by your, or someone else's
unbalanced load.