It is said that Henry passed this law because he wanted to divorce his wife in order to marry someone else, but the pope refused(citing canon law I think) to grant such an annulment. Henry Needed an Heir, because his wife apparently couldn't provide for him. Thus, the acts of supremacy were born.

You're on the right track here, but not quite there. The pope wouldn't grant Henry an annulment because he'd already been given papal permission to marry Katherine of Aragon in the first place: she had been his deceased elder brother's wife, and that was expressly forbidden by the church. (It would prove to be a pretty strong taboo over the centuries - there would be periodic challenges to English common law against the reciprocal prohibition against marrying your wife's sister, but for the most part people really internalized the idea that your brother's wife was effectively your own sister.) The dispensation went through on the basis that Arthur Tudor and Katherine had never actually consummated the marriage because of his poor health, which meant that the two never actually became one flesh and Katherine was never really, fully married.

Katherine gave birth to several children, but only Princess Mary survived infancy and childhood, and she was eventually recognized as her father's heir - she was never named Princess of Wales, but she was given a household in Wales and a princely education. A smooth transition of power from a king to his daughter was unprecedented in British history, but to all appearances it was what was going to happen.

There's a lot that could be said about the beginning of Henry's relationship with Anne Boleyn, so I'm just going to skip to the relevant part - he wanted to marry her for her, and also came to believe that God was signaling the invalidity and sinfulness of his marriage by not giving him an unproblematic male heir. It's not that he refused to pass the throne to a female one, but that wasn't really seen as normal or preferable. (And this is why Anne's eventual failure to give him a male heir was also part of her downfall - not "I need a son or there's nobody to inherit the kingdom" but "obviously this is a bad marriage too or I would have a son".) This conflicted with the pope's refusal to grant the annulment, which was on the basis that there was no impediment to Henry's marriage to Katherine (since the one impediment had been dispensed).

So declaring the Act of Supremacy 1534 justified or unjustified depends on one's perspective. From one viewpoint, the pope's refusal went against God's will and therefore made it right for Henry to break from this illegitimate church; from another, Henry should have allowed the pope to interpret God's will for him and not asserted that he was better equipped to know what was correct. There is no objective determination here.