Well, i dont think that Akira Toriyama ever really gave an exact answer to this question.
However he DID give an answer to the female saiyans and their potential, on which he said that female saiyans have just as much potential of becoming super saiyans as males, however why Pan never became one is all speculation, i myself either think that she had too little saiyan in her (1/4) or that she never really got to it, technically being the weakest fighter of the saiyans on earth.
Now about Goku and his super saiyan status. Akira Toriyama first wanted Goku to be the only super saiyan, because he wanted the series to end after Namek, and thus making Goku the only Legendary Super Saiyan in a 1000 /10000 years depending on the dub, but due to pressure from fans be continued and had to change a few things, one being the myth of the super saiyan. Fans speculate that Gokus transformation wasnt a ''true'' super saiyan but a kind of unpure version, where the only Legendary Super Saiyan we see is Broly. This Legendary Super Saiyan is based on some kind of magic/preselection of sorts where it would already be in the cards that Broly would turn into the Legendary Super Saiyan at birth, due to his wierdly enormously power level at 10000 as an infant - he was the guy the legend was talking about... not Goku or anyone els of the Saiyan race.
If we ignore DBGT, which many would call non-cannon, then the other theory (and mine aswell), is that a SSJ is not something mystical, legendary, magic or anything of those sotrs, its simply a technique thats very difficult to learn, and due to the very, very few saiyans who learned to do it, the story became legend. theres no doubt that Goku (as well as the other saiyans on earth) are very different from out typical saiyan we see in flashbacks or the likes of Raditz, Nappa and eairly Vegeta, because of this Goku and CO. may have had a much better starting point to learn how to do this technique.
Look at it this way: In the legend of the first SSJ, its known that he was the only one (at the time at least) and that he quickly became a martyr, he only wanted to gain power, so most cleary he wanted to keep his new learned technique for himself. Goku on the other hand was very different and spread his knowledge.
On another note, i personally think the whole ''you need a clear heart'' is BS, its about tremendous physical and mental training and pain.
Now im personally fan of the other SSJ versions (1,2,3... 4 is okay i guess), i think that its just are a better control of the standard SSJ technique. Now one thing i hate is how uncreative Akira was with the names.. ''LOL. imma call it Super Saiyan 2 and 3.. trololol''... thats so god damn stupid. Why not call it ''Divine Saiyan'', ''Prime Saiyan'', ''Golden Saiyan'' or something.
Like first Goku goes Super Saiyan, then learns to go to Super Saiyan Prime, then Golden Saiyan and then Supreme Saiyan or something, meh i dont know, but it surely sounds better than just going Super Saiyan 3.
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