There's a grain of truth in here, but not quite. One in every four or so (not quite, but we can roll with it regardless) identified species of animal is a beetle. Not one in every four animals, by population nor overall species.

The reasons for this is are many, but may include because beetles are big, easy to catch, agriculturally-significant, and are particularly easy to pin and study, dramatically boosting the count of beetle species we work with on an academic level (lending to higher identification rates). There are also just a shitload of beetle species, naturally.

Scientists estimate something closer to ~10 million species of animals, which would still make beetles a huge percentage of the species, but a far cry from 25%. If you looked at the total number (estimated) of individual animals, beetles are pretty insignificant.

Source: Studied entomology and love me some Coleoptera