In many kung fu sets, one hand is emphasized in attacking an opponent (the “emperor hand”) while the other is emphasized in defending or taming an opponent (the “minister” hand). There are several reasons for why the majority of kung fu sets are not ambidextrous.
Many kung fu sets will have a pattern occur just on one side. For example, the Old Yang family 108-Pattern set that I learnt does Grasping Sparrow’s Tail and Single Whip on just one side. The Southern Shaolin set Cross-Road at Four Gates reserves the left hand for sweeping and spear-hand thrusts (where the fingers are protected and strengthened through force training) and the right hand for fists and claws. Tantui’s opening and closing pattern, Sun Emerges From Clouds, is generally only done with the right fist and left palm.
Those masters that I’ve trained with that could actually use their kung fu for fighting remarked to me that many times, a student would have a firm foundation using techniques on both sides before later “specializing” in some fashion. The main argument was that at the higher levels of life-or-death fighting that occurred in China’s past, it would be more cost-effective and require shorter time to get a desired result (e.g. striking power or adroitness at deflecting or dodging).
My great-grandmaster, sitaigung Ho Fatt Nam (who had learnt seven other fighting styles before choosing to practice just Southern Shaolin in his later life), remarked to my grandmaster that, “You do not need to learn to write with both hands.” My own master remarked that in many of these sets, the average’s person’s natural strengths are emphasized (e.g. a right-handed person’s fist is often naturally more powerful than their left fist) while weaknesses (e.g. a right-handed person’s left hand) are shored up in some fashion, e.g. trickiness, speed, sensitivity, or special force training.
Conversely, some kung fu styles are more well known for ambidextrous techniques. Choi Li Faat (Cai Li Fo)’s famous “Whirlwind Fists” tactic is often trained on both sides. Baguazhang literature is replete with admonitions to train both sides so that one can be fluid on both sides, and I myself practice circling, dodging, and flowing to both directions.