> The difference is that UBI would be something like a right
The notion of a right does not include material implementation of that right for you by others, it merely states that you have a right to earn it and keep it by your own work and effort.
The right to counsel is more about what the prosecution can't do (sentence you without giving you a reasonable chance to defend yourself) than it is about something other people owe you just for existing. It's there because sentencing you when you didn't have the benefit of competent counsel to make your case would call the legitimacy of the court's judgment into question. Note that it only applies when you are the defendant, not the plaintiff, and you can't claim your right to counsel just because you need someone to help you draw up a contract. The right not to be sentenced without the benefit of counsel upon being accused of a crime is a negative right.
The idea that other people owe you specific goods or services just for existing—a.k.a. positive rights—leads directly to contradiction and conflict.
The notion of a right does not include material implementation of that right for you by others, it merely states that you have a right to earn it and keep it by your own work and effort.