John F. Kennedy was NOT pictured in his official Presidential Portrait.
In fact, it was his brother, Robert Kennedy, who posed for the painting. That is the reason for the downward looking pose. The eyes would have given Robert's identity away. Some people see in the portrait as the burden of the office on a young president as America was about to enter darker times.
The portrait is very different to every other official presidential portrait ever created. Some see in it a feeling that the painter knew what was coming for the United States. JFK, and his brother were both famously assassinated early in their political careers.