Dialga was injured as well, but he still wanted to kick her ***. He saw Palkia as a coward for running away from him so that's why he was angry.
Where are you even getting your canon/fanon? :/ In the movie, Palkia was the one who was seriously injured, not Dialga. There was nothing that stated Dialga thought Palkia was a coward, and to top everything off, I'm pretty sure most people think that Dialga and Palkia are equal-footed in terms of power. I have yet to find a lot of people who say otherwise.
However, why is it okay for girls to be overpowered and beat boys and be all like "GURLZ RULE! BOYZ STINK!!11!" but when a male Polkemon is stronger than a female Pokemon, then it's wrong?
No one's saying you should have your girls be overpowered. However, most of your girls are weak. Giratina's childish, Hydreigon is a stereotypical (and potentially delusional) damsel in distress, and Palkia is basically Princess Peach. Sure, we have Gothitelle from you, but she's not a prominent character in your work. She's also only one true strong female; the other "strong females" are all basically background characters. Instead, we get either cutesy females or females who insist on being the damsels in distress, neither of which are realistic or something real girls can relate to.
Even Princess Peach could help herself out of a situation. Think about it. In her game, she might have had a magic parasol to help her, but ultimately, she won the day using her own (literal) inner strength. Mario didn't step in to stop Bowser for her, and he didn't lend her his power to do it. She did it on her own. Moreover, she went out with self-confidence. She
insisted on taking on the mission to rescue Mario. She didn't simply sit around and wait for someone to push her into action or for someone to save the day.
That's the problem most people are having with your characters. They're pretty much sexist. Two of them would rather wait around for a man to save them instead of act on their own, and then you have Giratina and the other cutesy ones who imply that women are only good when they're being cute or femme. You don't have to be overpowered to be a strong female character. People fight their battles in different ways.
For example, look at the characters of
Sailor Moon. Sure, you have some of the girls (like Moon herself) who dream about being frilly princesses who will be whisked away by princes, but then you have characters who kick tail and take names, not necessarily literally. Sailor Mercury is probably the prime example of this. Check
this battle out. She doesn't fight against that particular monster with brute force. Instead, she calmly thinks things through and outsmarts her opponents.
Another example? The only character who ever equaled Sherlock Holmes in terms of intellectual prowess (besides Moriarty) was Irene Adler --
a woman.
Then, if you're not interested in writing a genius (who isn't necessarily perfect or the strongest physically), there's plenty of other female characters who aren't weak and aren't overpowered. May's actually a good example in Pokémon canon because she can win her own battles and stand on her own without Ash's help. Iris is another one, although she's not exactly excellent at battling (outside of game canon). Heck, most gym leaders in general are actually prime examples. (You could even go one step up and look at Cynthia, Karen, or the other higher-ranked League members.)
Point is, it's possible to be a female character who can work things through on her own without being overpowered. However, most people have problems with your characters because at least two of them only want to be rescued by other people, and a number of the others just act like children. In other words, at the beginning, they're extremely weak. The strong or otherwise capable females either get pushed off to the side or (in the case of Giratina's mother) are portrayed as sociopaths. It's the males in your fics who kick tail and take names from the get-go.
Then, your story ideas don't even really imply that a female character ever actually becomes strong. For example, in this fic, Palkia never uses her own power to defeat Ghetsis. She has to borrow power from Dialga in order to do it. This differs from Princess Peach, who has everything she needs within herself. Peach
doesn't need to call on Mario's jumping ability or Mario's other forms in order to take Bowser down. So, Palkia never truly gains confidence in herself, and she never truly gains the power she needs to get the job done. She's only reliant on Dialga, which sends readers the message that women can't do anything without the assistance of a man. (As a side note, Palkia can't learn Assist, so there's that as well.)
In other words, the final answer to your original question is... you can't. Not with the kinds of trends you've been showing in your work. In this case, you're implying that there's very little character growth, and there's nothing really to be learned. Palkia starts as a damsel reliant on men, and she ends as a damsel reliant on men. Considering that's basically one of the three major types of women you have in your fics (the other two being the background characters and the naive ones) and considering the fact that many of your men are knights in shining armor or warrior characters, yes, it's wrong.
Or in shorter, having one or two of these kinds of characters is fine so long as you have the character gain enough strength (inner or outer) to stand on their own. Having an entire universe of stagnant characters or walking tropes who are always reliant on others is not fine because the world (and character growth) doesn't work like that.
Or in even shorter than that, the point isn't to have female characters who always defeat boys. The point is to have believable characters who eventually experience character growth, regardless of gender. Except you have a tendency to hamper your females' abilities to grow for frankly ridiculous reasons.
And I do apologize for how biting all of this is, but I will have to be frank and say that I have an inner feminist who gets bitey at these kinds of things.
Stats, anime and fandom all point to Dialga being stronger than Palkia.
Um... no.
Base stats of both dragons add up to 680. Both of their base Attack is 120, and their Special Attack stats are both 150. Dialga's Defense is 120 and Special Defense is 100; Palkia's is reversed. Palkia's Speed is 100 and HP is 90; Dialga's is reversed. So, literally, they have the same stats in different distributions, and Palkia can score just as hard hits
faster. Moreover, both are considered uber-tier Pokémon, and it should be noted that whereas Smogon (
the competitive battling site) states that Dialga is
hard to counter, Palkia
has no true counter. (Granted, this is in Gen IV, but still.) The only leg-up that Dialga has over Palkia, really, is the fact that it's Steel/Dragon, but Palkia has counters for that.
In fanon, as I've said, Palkia and Dialga are typically seen as equals. That's how they actually are portrayed in canon. The anime simply had Dialga score a lucky shot, but otherwise, there's absolutely nothing that indicates one is stronger over the other.