One of the hands I least like playing is A2 offsuit. If I'm in the small blind, and the big blind has like 3 BB left or something, then of course I will cheerfully shove. At a depth of say 12 or 13 big blinds it gets a little more murky, especially if many players will incorrectly call you will small Ax combinations. Any pair that calls you, then you are of course in trouble.
Post flop play gets tougher. Any Ace that calls you is going to have you out kicked if you pair your Ace on the flop. Also, depending on the flop, you cannot be all that happy about C-betting with a pair of 2's.
If you make a full house, your 222AA could lose to say 888AA, or AAA22 can lose to AAAJJ.
When you make a wheel, you will always have the idiot end of the straight. A3s and A4s I would be happier to play more aggressively in the right circumstance.
I'm not saying that it's an automatic fold, but I really don't like it in a lot of situations; and if I choose to play it I do so cautiously.