Performing a free standing handstand push up takes work. A LOT of work. If you are not doing gymnastics on a regular basis significant specific time will need to be spent practicing and training the strength for this movement. We practice things a lot in CrossFit. It is often hard to choose where to put in the effort. The Olympic lifts take a lot of time. Getting the mechanics down for efficient bodyweight movements takes a lot of time. With a lot of practice things it often just takes 5-10 minutes a day, but you have to be consistent with the practice and as Emily C. put it “I’m running out of 5 minutes”.
I have a particular bias toward this movement. I’m pretty good at handstand push ups, and in my sport being able to perform a solid handstand push up free standing is essential, and an eventual byproduct of the normal training. I am always encouraging everyone to aspire to making this movement, but few accomplish it. It is a very lofty goal. On par (possibly harder, I don’t have the best perspective on it) with a bodyweight squat snatch. Working in this direction can be frustrating because the scales aren’t just a change of weight, but a modified version of the movement, so progress isn’t as easy to measure as a weightlifting movement.
I wrote a CF Journal article which gives great detail on the progression. Here’s the repost on DrillsAndSkills.com.