With old money, reversibility is handled by return policies, merchant account charge-backs, liens, and civil lawsuits.
If you hand a bearer instrument like a bank note to someone, that transaction is technically irreversible. They put it in their pocket, and you can't recover it without a physical assault. You have to trust them to provide the goods or services that you just paid for. Or you have to trust the justice system that it will allow you to (eventually) recover your payment if the other party reneged. These remedies are often not available with cryptocurrency. You may be unaware of the counterparty's physical location or true identity, and even if you did, they may be in a different legal jurisdiction altogether. You can't round up a posse to go get the money back.
If you pay with a finance system account, you can dispute the charge with the payments processor, and your payment may be reversed by them, even after the cash balances have already been altered, by withholding payment from a future transaction through that processor. Criteria for reversal may vary between processors. If consumers trust the reversal policy of the processor, the merchants get more money, because consumers don't have to trust them or the formal justice system. They can get refunded now, and let the processor and the merchant argue over the details. This remedy is available to cryptocurrencies. While individual transactions are irreversible, it is possible to redirect future transactions through a trusted intermediary or a smart contract.
Basically, everyone wants an escrow mechanism of some sort built in to the system, so that if a customer doesn't get the goods or services, the merchant doesn't get their money; and if a merchant doesn't get paid, the customer doesn't get goods or services. As long as the transactions are irreversible, someone can get ripped off, and they have to go out-of-band for a remedy. As long as transactions are trivially reversible, someone can get ripped off, and they have to go out-of-band for a remedy.
Conveyance of money and delivery of goods or services are each half-trades. We don't like those half-trades. They're too much like gifts, in that there is too little ability to enforce reciprocity without a preexisting social link. If you conduct business in half-trades, you still have to trust, and people can still get ripped off. So far, cryptocurrencies only technologically validate the money-conveyance half-trade. What it needs is a way to validate the other half-trade, for goods or services, and bundle them both into an atomic whole-trade that either reverses or becomes permanent as a single unit.
Trade chains would be nice, too, but atomic transactions are what people need to trust the system instead of trusting each other.