Sometimes this happens because people are on their phones or otherwise zoning out, and only realize it's safe to cross when somebody else starts doing it.

But I think the big reason this happens is because, if someone else starts crossing the road, then it must be because either nobody is coming, or because the drivers on the road have already indicated their willingness to yield to the pedestrians. In the latter case, it makes sense to cross directly behind somebody else who is crossing, because a yielding driver provides a short window of opportunity for crossing safely.

In general, watching somebody do something that you thought was risky tends to be a subconscious prompt at the thing was perhaps not as risky as you thought. It's a little more subtle than "animal brain bad, look at the lights you dummy".