> you must surely be guilty of something. Otherwise, all offers would be meaningless and worth nothing.

You don't have to be "guilty" of anything to be liable in civil law (which contract law is a part of). "Guilt" is a concept from criminal law. It isn't required for contracts to be enforceable.

In general (there are exceptions) offers alone aren't enforceable and don't result in a contract. You need other elements (agreement by the parties, plus something done in return for what's offered) for a contract to be formed - and then it's enforceable.