The problem with logical positivism was that it contradicted its own theories! Their definition of a philosophy included the fact that a theory or idea must be based on observable data or is meaningless. The three requirements they gave were, a. true by definition, b. testable, and c. true by experience. Their own there does not for their requirements!
The other problem was that, for example, religion. They said that religion is no more than an expression or emotion and idea because it is not verifiable. But who is to say what one’s experiences are? Why can’t I say that I saw God and have it be an experience?