Sorry, I should have said "profit path", good catch!
They have revenue, but their cost scales with revenue and they're losing more than they are making.
Their costs do not scale linearly with revenue. Inference is expensive, but it's a variable cost. Anthropic's overall costs include massive fixed costs in training, which are the same regardless of usage.
It's easy to falsify the claim with a simple experiment: imagine they had no customer at all, $0 in revenue. Their costs would still be massive. If the claim were true, $0 revenue should mean $0 costs, right?
That's convenient accounting. The reality is that they can't stop training since they risk losing customers if they do so. So they shouldn't factor it out of profitability analysis.
See: https://www.wheresyoured.at/brokenomics/ for an interesting write-up on the economics of AI.