How is pointing out that people who don't own cars need ways to get around a strawman? It directly undermines the point you were making.

Most urban cyclists are not rich white men. The Lycra crowd usually sticks to recreational trails or more rural or suburban roads.

Edit: just to add some data here.

A better way to look at the distribution is to consider the median income of bike commuters, relative to other commuters.  The median bike commuter had a household income of about $72,000 according to this data series, meaning about half of all bike commuters have household incomes less than that amount and half have more.  To put than in context, the median car commuter had a household income of about $82,000.  So, on average, bike commuters live in lower income households than car commuters.  For reference, the median bus commuter lived in a household with an income of about $62,000.

TLDR it's actually car commuters that are the wealthier demographic. So if your concern for the poor was genuine, you would support more bike lanes. But somehow I doubt you will change your tune...