They definitely do not have the same chances, abilities and opportunities to succeed as other children do
Who are these 'other' children? The ones you are selecting to compare your kids to? A non-standardised selection that include children who had wonderful life?
This goes back to my point that too many assume that those who 'succeed' had easy life and were therefore lucky. Some will and some will not, just as some kids will have a great start in life and still face unexpected hardships that they will have to overcome to do fine.
Our problem is that we are constantly comparing ourselves to selected others to suit the position we see ourselves in and if that is to feel that we are hard done by, will inevitably mean comparing ourselves with people who at that particular time appear in a better position than us.
Those who have the perfect life could become the ones we would envy the least tomorrow, the ones who are faced with the unfairness of life, despite having it really good until then.
We could almost all consider that life has been unfair to us, be it because we started in poverty, because we are not physically attractive, below in intelligence, because we never met anyone that made us happy, couldn't have children, had to look after demanding elderly parents that prevented us from living our own life, because of expected or unexpected health troubles, or disasters in life.
So I do fully agree that no matter the unfairness, almost everyone has an opportunity to make their life a bit better at some point in it but for that, we have to focus our attention and energy on times ahead of us rather than the past and present.