Why are retained earnings reported as part of shareholders' equity?

Retained earnings is part of shareholders' equity. It is considered part of equity because it represents the profits that are retained in the company to fund growth. If a company would have paid out all past profits as dividend, then total assets (cash) would be lower, and retained earnings would have a zero balance.

Because net income is computed after claims of third parties (interest, wages, etc), there is no claim of third parties on profits that are retained. So, retained earnings are not a liability.