When a poor man invests in a bicycle to increase his wealth, he's taxed regardless of outcome. When a rich man invests in stocks, he's only taxed if he profits.
If you view the bicycle as an investment to buy and resell later, then the poor man can claim a capital gain or loss on sale. If he claims a loss, he would pay no taxes on it, and could potentially offset prior or future income with said loss.
Otherwise, a poor man pays no taxes on the purchase of a bicycle (except sales taxes in some states, but talk to the state governments about that).
If you're talking about the money that was used to purchase the bicycle, well, think about it. The poor man would have received money from a job he worked, paying taxes on it (or maybe not if he had enough deductions). The rich man would have received money from prior investments, which he did pay capital gains taxes on.
So what's your point? How are you correct in what you said?