I can't believe I didn't see it until now. The dollar is some SovCit level legal woo. He probably thinks if she accepts the dollar, that makes his offer for a date legally binding
He probably got it from a unit in contract law. In Common Law countries (the USA uses a modified and localized form of Common Law), any agreement can be a contract, but only certain contracts can be legally binding. IANAL and this is all from memory so excuse any mistakes.
$1/£1 is the smallest denomination that can be used as consideration in a contract. A contract, to be legally binding, must have several elements:
1. Parties that are legally competent and able to freely give consent without coercion or duress. Minors, intoxicated or persons judged to be legally incompetent cannot enter into a binding contract.
2. A lawful object. If I wanted to sell someone a kilo of cocaine, and they gave me a duffel bag of cash and it was less than the agreed upon price, I couldn't file a civil suit for the remainder, as cocaine is illegal to possess or traffic.
3. Consideration. Both parties must get something of value.
4. Clear terms of fulfillment. If I loaned a deadbeat $2000 and I told them to pay me back when they can, It wouldn't stand up in court, as there are no clear terms, and no reasonable expectation that I will be able to recover the money.
For example, if I were rich and old and had several houses and a particularly deserving nephew who was 33, I could give one to him, but it would be much easier if I were to sell him the property and the title for $1.
The elements are all there: He and I are both legally competent. The house is a lawful object. $1 is consideration (he gets a house, I get a dollar, we both get something), and there are clear terms of fulfillment- the contract is fulfilled when the sale closes and the title transferred.
cRusty thinks that if the girl takes his dollar, that's his magic ticket to make his date offer legally binding.
However, it fails all 4 tests- he is deceiving the girl and threatening her with defamation if she does not accept his offer, a date cannot be specified as a particular service or quantified via monetary value, and there is no clear definition under which one can define a "date" as having been performed.
TL;DR: cRusty thinks that if the girl accepts his Venmo dollar, she is entering into a legally binding contract to go on a date with him. That isn't the case because reasons.