They are supposed to be the way we take in data, no? So how can something that relates to input be directed outwards?
As a side note, the modern cognitive functions model — which involves a set of function descriptions that were essentially jerry-rigged to match the MBTI types that they purportedly correspond to — says you "extravert" your perceiving function if you're a P, rather than if you're extraverted, and I'd say the characterization of those SP-ish and NP-ish characteristics as "extraverted" is arguably more than a little strained.
Buuut if it's Jung you're talking about — and I'd say it's primarily because the modern cognitive functions gang like to position themselves as
Jungians that Se and Ne are framed as "extraverted" functions — Jung's model of extraversion and introversion didn't exactly involve inward-direction and outward-direction in the way your post pictures them.
Instead of thinking of a model with two things (the subject and the object) and E/I as the direction of the arrow that points from one of those things to the other, think instead of a model with
three things: the collective unconscious on one side, the external world on the other, and the subject in between.
Now, with that second model in mind, think of extraverted perception as involving the subject
turned outward, taking in data from the external world, while introverted perception involves the subject
turned inward, perceiving the data (archetypes, primordial images, etc.) from the collective unconscious.
In both cases, the subject is "taking in data" (as you put it), but in the case of the Pe functions, the
source of the data is external.