No, every finite hypermetric space is embeddable into an ℓ1\ell_1 space.

Background:

• Schoenberg's theorem and subsequent work by Deza and Laurent (see their classic book Geometry of Cuts and Metrics, 1997) show that: Every finite hypermetric space embeds isometrically into an ℓ1space.

That is, hypermetricity is a necessary and sufficient condition for ℓ-embeddability for finite metric spaces.

Conclusion:

✅ Every finite hypermetric metric space is embeddable into an ℓ1 space. ❌ So, a counterexample (a hypermetric finite space not ℓ1 embeddable) does not exist.