Both my shoulders dislocate randomly, what's the problem?

Suggestion: Assuming that you suffer from anterior dislocations, i would recommend physical therapy. Also, concentrate on the exercises for shoulder... If you are doing push-ups avoid going deeper than 90 degrees at the elbow since this will put your shoulder in a vulnerable position for dislocation. Avoid tricep dips for sure! if conservative treatments do not work, you may need surgery.

Ligamentous laxity: Certain people have ligamentous laxity of the shoulder. If your dislocation have all been non traumatic from the start this may very well be the case. Physical therapy can help and avoiding certain positions or activities can decrease the amount of dislocations. Get evaluated by an orthopedic surgeon who specializes in shoulders to start. Avoid voluntarily dislocating shoulder.