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".
There's also a benefit in visibility. Even if you fix everything else constant (same number of cars, at the same distance, etc.), it's safer to cross the street when someone else is already crossing than it is when no one else is crossing. It makes sense that someone being willing to cross at a red could push others over into deciding to cross.
Or there is a car coming and it isn't slowing down but there is just enough time for me to nip across in front of it. Maybe this doesn't happen in countries with jaywalking laws, but it does happen here.
How many traffic laws and safety practices did the three cops break to surround and arrest you in the middle of the road? Oh, but that's their job. Not yours.
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".