In my opinion, the most reasonable claim is that blockchain is a decentralized system that allows people to conduct transactions without a middleman. Blockchain technology allows people to make transactions without having to go through banks or other third parties. This means that you don't need to pay fees for using the service and your data isn't being sold (or stolen) by a third party.
The most unreasonable claim is that cryptocurrency will replace fiat currency as the main form of money in the world. While some countries have begun accepting Bitcoin as legal tender, it's still nowhere near as widely accepted as regular currency. In fact, many countries have banned cryptocurrency altogether.
I feel like there are a lot of reasonable and unreasonable claims about blockchain and cryptocurrency, but the biggest problem is that people don't understand the technology. I think it's important to look at what blockchain is, what it isn't, and why people say it can do things that it can't (or shouldn't).
Blockchain is a distributed ledger. It's a database that everyone has access to, but no one can edit (at least not without consensus from all participants). That means that if you create something on the blockchain, you own it—no matter who tries to change it or delete it. And when I say "everyone" has access to this database… I mean EVERYONE! That includes your grandma and even my dog.