It helps him that he's more of an entrepreneur.  A really bad one, generally, but one nevertheless.  Whereas Fiorina's more the MBA-type, so she doesn't really have the brand that goes along with an empire, however shitty that empire that may be.

I assume she did something at least half-decent to get the HP job while she was at AT&T and (I think?) Lucent.  In that sense, kinda like Trump:  One decent effort followed by colossal failure everywhere else.  Trump was just savvier in turning his real business into a brand.

Be nice to America. Or we'll bring democracy to your country.

Obama, who tends to be pretty levelheaded and tends to roll his eyes at obvious politicking like this, was reportedly livid.  He didn't respond in public but did apparently give her a piece of his mind in private.  Axelrod, on the other hand, had no qualms about responding on Twitter.

I'm sure there were situations like that, where she'd advocate a larger response and he'd veto it under the "Don't Do Stupid Shit" doctrine.  And I'm sure it did chafe her.  Clinton tends to favor sweeping ideological positions in the foreign policy realm that suppose our military and intelligence folks are capable of a lot of social engineering.  Obama tends to be skeptical of sweeping ideological positions on anything (he's a liberal, obviously, but doesn't tend to be wedded to methodology), doesn't think large-scale military interventions like Iraq are either necessary or desirable, and prefers calculated risks on an ad hoc basis that leave us with an ability to wind down or ramp up as results dictate.

(His interview with Jeffrey Goldberg was pretty informative on that.)

If she's smart, she'll see that it served him pretty well.  It's how he beat her eight years ago, after all.

Be nice to America. Or we'll bring democracy to your country.