It actually makes sense. It's not about age. Middle management has an expiration date. If you've been a middle manager for 15 years, that's bad bad bad. (Being an IC for 15 years is respectable; but once you move into management, you should make director in 5 years and VP in no less than 10.)

Programming has an ageism problem largely because it's run by career managers (who think all of us want to be them-- and we don't); engineers themselves aren't ageist. Management is where the ageism comes from and it's even worse in their world. It's not that they care about age so much as they want to avoid hiring terminal middle managers, and I can't blame them for the latter. This fact has absolutely nothing to do with age, but terminal middle managers are toxic.