The Concept of Pressure in Bernoulliís principle
Part of the confusion here is due to the fact that there is more than one type of pressure and people/articles are often sloppy about which they are referring to. Often when people say "pressure" they are referring to static pressure. But there is also velocity pressure and total pressure. In Bernoulli's equation, when velocity increases, velocity pressure increases and static pressure decreases, while total pressure remains constant.