Based on personal experience I don't believe it has as much to do with smartness or willingess to work hard. A lot of poor kids have that too.
The bigger difference is that successful parents are constantly acting as role models, giving their children cues to follow, and passing on important knowledge that schools don't whether they realize or not. Many poor kids miss out on those things entirely, and as a result end up spinning their wheels later in life due to misplaced efforts and fumbled attempts. They may eventually figure things out on their own, but it'll happen several years down the road, and while they can narrow the gap closing it entirely becomes more difficult the further they ascend (feels a bit like Zeno's Paradox).
The bigger difference is that successful parents are constantly acting as role models, giving their children cues to follow, and passing on important knowledge that schools don't whether they realize or not. Many poor kids miss out on those things entirely, and as a result end up spinning their wheels later in life due to misplaced efforts and fumbled attempts. They may eventually figure things out on their own, but it'll happen several years down the road, and while they can narrow the gap closing it entirely becomes more difficult the further they ascend (feels a bit like Zeno's Paradox).