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As far as I know, you must be strictly less than 20 years old in order to participate. I don't know about any minimum age limit.
An excerpt from IOI R&R:
N2.5.2 The age limit for contestants may also be defined as: Every contestant at IOI’n (held in year ccyy) must have been born on or after 1st July, in the year ccyy-20.
E.g. your 20th birthday must be no sooner than on the 1st July just before the corresponding Olympiad.
That's all there's mentioned about age in the R&R, so there's no lower limit on age. Of course, specific countries can impose their own limits on the participants (in a certain olympiad in Slovakia, a lower limit was imposed because they didn't want a certain person to participate, for example).
Imposing a lower limit to prevent somebody from participating? Sounds strange, what were the reasons to do that?
He was able to, for example, leave the group on an excursion and go where he wants. With a minor, it's serious trouble for the leaders if something happens to him, so they decided to not take any risks and "legally" kick him out of the competition. Humans can be strange sometimes.