Why Was Hagrid Left Out of the Order?

[entropymail]

No: HPFGUIDX 109748

Okay, guys. Here's one that's been niggling at me all day and, I'm
sorry to say, I don't yet have any answer for it.  The question is:

"Why isn't Hagrid in the Order of the Phoenix?"

Well, of course, my first reaction was to believe that it was because
of his lack of magical talent and training.  But then I remembered
Arabella Figg.  She's a Squib, for goodness sakes, and they let her in!

Then I thought perhaps Dumbledore felt that Hagrid's ...erm...lack of
discretion at times, might be a good reason to hold off on his invite.
 But if we're going to exclude those of questionable
discretion/character/loyalties, then certainly good ol' Mundungus
Fletcher would be a bit more questionable than Hagrid ever would.

So, what's your opinion? Why hasn't Hagrid been invited into the Order? 

:: Entropy ::