That is a terrible analogy. Beef CANNOT TURN INTO horse meat. But "bitcoin" did turn into "btc + fork"
Private keys -- not bitcoins. Bitcoins you have on deposit are completely unaffected by the forks. And you don't control or "own" the exchange's private keys. I'd be curious to see your argument made in court, but it's definitely not a slam dunk in my eyes.
I imagine that whether there is a legal basis may be moot. If many persons pool together and sue the exchanges, the easiest way for them to resolve the issue would just be to release the forked coins.
It's not cheap to mount a class action, and some of the exchanges are structured to make legal claims difficult. I think Bitstamp and Coinbase are good examples of how compliance-minded exchanges view things. If there is significant customer demand and market value (as was the case with Bitcoin Cash), they'll release the forked coins.