For example, one struck the neck with a knife as one strikes with a sword, cutting the signs [trachea and oesophagus] at one time, without passing [the knife] back and forth or one placed the knife on the neck and pressed, cutting downward like one cuts radishes or squash until he cuts the signs, [the slaughter] is unacceptable.
So one has to draw the knife back and forth instead of pressing to cut the animal throat.
I am looking to understand why this is the case? Is it to minimize pain to the animal? Intuitively this is not so simple to understand. Cutting oneself with a paper (similar to "passing the knife") is quite painful while one often doesn't feel a small knife cut (similar to "pressing").
Or is it to avoid damages that would make the animal taref (unacceptable)? Or something else?
I am not asking about the subjective feelings of pain but rather for halachic reasons that were proposed (taam hamitzvot). I didn't find it in the Sefer Hakhinukh (451).