Pooping asks a child to relax completely, in private, with time. Daycare offers almost none of that: a row of small toilets without doors, other children watching, a teacher keeping to a schedule, and the sense that this is not home. For a child who is already wary of pooping, the choice to hold is an easy one.
Holding works in the short term. The urge fades, the day carries on, and the poop comes later at home, often with a big release at bath time or in bed. But each held poop dries and grows, so over weeks the home poops get larger and harder, and the child becomes more determined to avoid pooping anywhere.
Daycare staff may notice tummy aches, a change in mood in the afternoon, clenching or hiding in a corner, or the smell of a small leak. Often they do not connect these to holding, because a child who holds looks like a child who simply does not need to go.
Parents sometimes hear that their child should be 'fully trained' or that the daycare cannot help. In practice most settings will accommodate a clear, short plan, and the best plans are the ones where home and daycare use the same routine and the same calm phrases.