Because he had the Nemean Lion's coat, which made him practically invulnerable while wearing it. He used a magic item in place of armor.
One of the problems when using mythical figures is that their nature changes so significantly over time. What's true fo Homer's Heracles is not necessarily true for Euripides' Heracles, or Seneca's. So one needs to be clear which Heracles/Hercules you are talking about. There are probably other sources that are relevant, but here are a handful of specifics showing how this one issue changes over 1200 years:
1. The idea of the labours predates Hesiod (7th c. bce) but what was done with that idea changes:
2. 5th c. bce Bacchylides (fr. 13) first explicitly says that the skin can't be pierced. It's an element that probably exists before this, but here's when it occurs earliest, I believe. [In game terms, we might say it's resistant to piercing or slashing damage. Accounts have Heracles take a club or strangle the creature -- i.e. using bludgeoning damage.]
3. 3rd c. bce Theocritus (Idyll 25) first explicitly says that its claws can pierce the skin. [Compare the effect of the vorpal sword which can bypass slashing resistance but not immunity -- they effectively are vorpal claws.] Several later sources show that this is not the mainstream view; strangling is far more common, and persists through Seneca (Hercules Furens), Statius (Thebaid 4, 6), and on to Nonnus in the 5th c. CE.
4. 1st c. bce Diodorus (4.11.3) first explicitly says that wearing the lion skin offers some sort of protection (though with no totalizing claims). The claim is repeated in Hyginus Fab. 30 (2nd c CE), but I don't know of anywhere else. [This is similar to the benefits of the boon of resilience (Heracles by definition is level 20+), and cf. the armor of invulnerability]. Ovid, Heroides 9, says that he wears it on his left side, but not that it offers particular protection.
I think the reality is that most ancients didn't think in terms of optimizing Heracles in combat, because it was beyond question that he was extraordinary. To generalize about him, though, eliminates the complexity of ancient myth.