There's a bit of history behind all this.

The overhead lifts were traditionally considered the "prestige" lifts ever since the strongman era at the turn of the century - the way the old time strongmen like Arthur Saxon and Louis Cyr would compare their strength was simple: to lift as much weight as possible over their heads. Overhead lifting had the added benefit of being thrilling for the circus crowds, and there usually weren't any strict rules around the choice of technique - the most popular lift in those days was the bent press (often done one handed with a barbell while simultaneously lifting a kettlebell in the other hand!). Of course, the strongmen would also test their strength with many other types of (non-overhead) lifts, but it was the overhead lifts that were the records everyone really paid attention to.

Eventually, the overhead lifts that were popularized by the strongmen evolved into the sport of Olympic weightlifting, which became standardized around the two-handed barbell lifts. The bent press gave way to the clean and (overhead) press, clean and jerk, and snatch, which were the 3 standard lifts in Olympic weightlifting until the clean and press was removed in the 1970s because it became too difficult to judge proper technique.

Now when the clean and press, clean and jerk, and snatch became the 3 official lifts for competition, everything else was banished as "odd lifts". This is how the sport of powerlifting originated in the 1950s - the odd lifts were popular with bodybuilders and other strength athletes, and people formed their own informal odd lifts competitions. This eventually evolved into powerlifting (standardizing on the bench press, deadlift and squat), and the reason the overhead press isn't part of powerlifting is because it wasn't an "odd lift" - it was in Olympic competition as part of the clean and press, all the way up until the 1970s.