SOC 3 CEO? They may have rank and wealth, but little real social power. Possibly their lower class origins are held against them by their peers. Maybe they're profoundly autistic or utterly obnoxious. Maybe that their rise to power was largely to show them all!
But then Traveller bases your cost of living on SOC... And the game mechanic for wielding that power they rose to is...the SOC stat they don't have.
And it's definitely not "being obnoxious or autistic" because that's exactly what SOC is NOT representing: which is social acumen.
The game mechanic does not reflect what the game says it does. They are not consistent in using it as status rather than acumen. They are not consistent about what it actually means because they conflate wealth and status in many places, but not in all places. Like the Corporate career only provides one possible boost to your SOC, which is a +1 from reaching Rank 6 and the Merchant career likewise, only by reaching Rank 5.
Traveller has from time to time introduced optional rules for just buying your way to high SOC. Or failing to pay to keep your SOC. But that's never been a normal function of game play.
The career tables suggest very strange things about the "place in society" of people in Traveller settings.
The vast majority of people have no social mobility whatsoever. Their SOC is 100% based on birth apparently, since there is no way to improve it as a worker, colonist, belter, or scavenger. And even merchants and corporate officials can only get a very minor boost to their birth status from reaching the pinnacle of their careers.
The most upwardly mobile are Entertainers and Scholars, the only two careers that can get +SOC in both Personal Development and Mustering Out (and they don't need to be Rank 5+ to get SOC on mustering out).
Interestingly, Nobles on active service can't actually improve their status. The only +SOC bonuses come from mustering out.
Scouts have an entire Knighthood specifically for them in sourcebooks, but nothing in their career makes that a thing that could happen.
The Navy is apparently the most prestigious career, because Rank 5 characters are automatically bumped to SOC 10 (or +1 if better) and their Rank 6 is SOC 12 automatically. The Marines get the Rank 5 boost to 10 but nothing for Rank 6. The Army doesn't get the SOC 10 until Rank 6. Rank 5/6 characters can also get SOC bonuses in Mustering Out, but there is no possible change in social standing if you don't reach those heights.