Anyways, the article I linked above, Essential Components Weightlifting Technique: Part IV - More About the Jerk, is a very in depth look into the development of the jerk.
The long and the short of it is that over development of the shoulders and arms can ultimately be detrimental to the jerk. While pressing and push pressing are essential accessory exercises, especially early on in the training process of a lifter due to the development of overhead stability, the initial leg drive (for push press), and overall torso strength, they can hinder an elite weightlifters jerk if the exercises are more than 10% of overall training volume.
A couple of the reasons, among others, were as follows:
1) Greater upper body strength has the potential to lead to more of a reliance on using the arms too soon or too much as opposed to a reliance on the reactive strength of the legs. This can also transfer over to a premature arm bend in the pulls of both the snatch and the clean. The article stresses that it is better to have a "pear shaped" body, i.e. more developed legs than shoulders and arms. The reactive strength needed for the jerk starts with the legs and is the most crucial aspect.
2) The mechanics of the press and push press are different from that of the jerk, so a greater focus on the two former can detract from the technical progress of the latter.
Again, this is not to discourage the implementation of press and push presses, but to make you aware that as you develop as a weightlifter with adequate torso strength, the focus of overhead work should transfer from the presses to the classic jerk.
Off topic, here's a video below of some legit lifts for you to geek out to: