I'm not a statistician, but I see some obvious holes in your logic, and I think if you stop to think about it you'll agree.
Let's start by extrapolating the trends into the future. What do you think might happen in the next 30 years? Would it be possible for the percentage of white babies born to unwed white women to double? Would it be possible for the percentage of black babies born to unwed black women to double? If it's possible for one of those stats to double, but not the other, then using ratios to infer something about the strength of the underlying trend is obviously flawed, but that's exactly what you've done.
When dealing with trends within a population (such as the percentage of people getting an illness), it's common to use logistic growth models. These can be modeled with variations of the following function:
f(t) = C / ( 1 + p*e^(-rt) )
Where C is the carrying capacity, p relates to the population size at time 0, and r relates to the growth rate. This results in an "S" shaped curve where the observed rate of growth (derivative of the function, not "r" in the function definition) necessarily diminishes as the population approaches its capacity.
If you want to compare changes in sub-population statistics over time, you may want to consider whether there is evidence that each sub-population group has different carrying capacities, why that might be, and what forces might change the carrying capacity over time. Similarly, you would want to consider whether the sub-population groups appear to have different underlying growth rates ("r" in the model above), and what might have impacted that rate over time.