Why do women get tons of men to pick from even if we're dirt poor and men can get tons of women only if they're rich?

For 80% that is probably true. Not always for about 20% of the people who are more cautious.

Potential and personality are at least as important and many a rich man has found that marriage can be a predatory trap. Sincerity and supportiveness is as important in a woman as her physical desirability.