1)If you compare with string instruments like guitar,banjo etc as you say down strokes are naturally stronger, if you compare with bowed string instruments like violin down strokes are stronger and analogous the *movement* by the arm(s) with a squeezebox means that pull resembles down stroke or down bow and would adapt to the strong musical beat that way.
Now, there is more to it...
2)With squeezeboxes the bellows stabilizes itself on pull while it has to be stabilized by muscular effort on push. The 'problem' with this gets more evident the longer or more flexible the bellows are.
Bondonions for example can hardly be played energetically on push at all but 'our' concertinas act basically the same - it is easier and takes less effort to keep the bellows in order on pull and thus strong notes are easier to perform on pull
3) With all squeezeboxes the valves ( "pads") seal better on pull and with some concertinas it can be a real problem - particularly baritones where the low range pads always are larger and may have a tendency to leak on push because of that. Therefore also it is safer having real strong beats on pull
So - despite many players spontaneously may feel it more natural to use push for strong beats the above 1-3 motivates using pull instead.
Most people are about as strong extending as flexing the upper arms so it does not matter. Some work or physical training (bodybuilding) may result in flexion dominance but that is extraordinary so usually it doesn't matter for the body which you choose.