The problem with 'positive' liberty is simple. You can't have it without taking negative liberty away first- i.e. Universal Healthcare as a 'right'- you have to compel multiple levels of society via coercion in order to fulfill that right, thus weakening their negative rights to be free from such coercion.
For some reason, many people seem cling to a nebulous idea of 'government,' that is more a wish fulfillment mechanism than concrete enforcer entity, can provide positive rights without impinging on the more basic negative rights.
One of my favourite interviews is with Berlin[2] where he talks about why positive liberty is so dangerous.
[1] https://www.youtube.com/watch?v=pfhQhdA-zss Tom Richey with an intro [2] https://www.youtube.com/watch?v=TIP9IjJcZr4 Isiah Berlin interview on the ABC on freedom