I'm not the parent and I don't have any data, but I think he is saying that he thinks people in lower income areas tend to not be supportive of efforts to support bicycling and/or bicyclists.
Just based on my personal experience, I think there may be some correlation, possibly due to the fact that bicycle commuters tend to be from higher income brackets, and that lower-income folks often see efforts to support bicycling as both a symptom and cause of gentrification that does not do anything to help them personally as they are less likely to be bicyclists themselves.
> bicycle commuters tend to be from higher income brackets
In the United States, the income segment with the highest rate of bicycle commuting (1.5%) is those individuals earning $10k/year or less [1]. Workers from households earning under $35k/year are 10x more likely to bike to work than workers from other households [2].
Of course, this doesn't directly imply that bicycle commuters tend to not be from higher income brackets, but if you examine the US household income distribution [3], it seems probable; as of 2014, a third of US households have an income below $35k/year. The Census Bureau provides some data tools which one could certainly use to break down bicycle commuters by income category, but their interface gives me trouble.