We regenerate plenty. Our bodies are constantly regenerating. We keep growing new skin to replace old (dandruff is a simple example), damaged organs can recover (eg liver problems), and even exercising to increase strength involves regeneration (broken muscle fibres grow back stronger). We don't regenerate large external body parts in general, but we do regenerate some bits quite well - like the palms of our hands.

If you cut us, do we not bleed? Then clot? Then grow new tissue to heal the wound? Sometimes so that there is no evidence of a cut afterwards?