A cleric of a chaotic deity falls because he is following the God's teachings and not striking out his own path like a chaotic person should.
Gorum refuses to kill opponents who can't fight back or who surrender. That sounds an aweful lot like having a personal code you follow. Chaotic people aren't bound by codes, that's Lawful!
Suddenly, Gorum became Lawful Neutral?
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Where do you get that it is supposed to be tougher to live up to the standards of good than evil or neutrality?The definitions of alignments in the pathfinder core RPG do not say it is tougher to be good, it just says they are different.
"Good characters and creatures protect innocent life. Evil characters and creatures debase or destroy innocent life"
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The Core Rulebook shouldn't HAVE to say this, but it is easier to destroy than to create or preserve. It should be obvious, starting with the very basic example that you can't unscramble an egg, and proceeding up the food chain to observe that cheaters, predators, and parasites get ahead if not checked.
What part of the Hero in Heroic Fantasy do you not get? If you really think that Good requires no more effort than evil, you not only do NOT get the genre, you've missing out on a lot that's been happening around you the bulk of your life. And if you are truly that unobservant, than there is absolutely nothing further I can say to answer you.
Flipping that question back to you. If you ARE that good and awesome, then why would you intentionally be doing evil? It's supposed to be tougher to live up to the standards of Good as opposed to Evil or Neutrality... just like it is in the real world.
If you're looking to operate on the modality that Good and Evil are nothing more than two flip sides of the same coin, you're not operating under the default assumptions of Pathfinder, and certainly not Golarion.
Where do you get that it is supposed to be tougher to live up to the standards of good than evil or neutrality?
Nonsense.
Pathfinder is set up to make it easy to be good. Written adventures are full of opportunities to help others, fight evil, and do good. Characters' jobs are often to do good. Magic mechanically rewards good over evil in many ways, a holy sword is more likely to get its bonus than an unholy sword in most adventures. Good and evil alignments are defined in the game and the good standard is not difficult to attain. Protect innocents, work for good causes, be the hero doing good in adventure stories often designed for heroes to do good.
As I quoted from the definitions before "A creature's general moral and personal attitudes are represented by its alignment". If your general moral attitude is good, you are good alignment in pathfinder. It is not a hard struggle to roleplay a good character in a Pathfinder game.
This is in keeping with the heroic fantasy genre. In the Lord of the Rings for the heroes, the fellowship of the ring, it was easy for them to be good. They volunteered to try to save the world from evil. Only the corrupting ring made it significantly difficult and this only really caused moral problems for Boromir when he tries to take it and for Frodo at the end (and the minor power temptation scenes for Gandalf and Galadriel). Aragorn, no problems. Gimli, no problem. Legolas, no problem. Sam, Merry, Pippin, good throughout. Gandalf is good.
You want a game where it is tough to be good check out Vampire. While pathfinder could be played as a Game of Thrones style game with lots of brutality, corruption and incentives for moral compromises, the default of Pathfinder makes it easy to be a good hero.
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Pathfinder is set up to make it easy to be good. Written adventures are full of opportunities to help others, fight evil, and do good. {. . .}
They might have set it up to be TOO easy to qualify as good. Actually, this goes back all the way to 1st Edition D&D (probably Basic/Expert/etc., but I'm not familiar with those beyond Basic and a brief glance at Expert). In our world, people do Evil because it works (for them, not for everybody else) -- if crime really didn't pay, many of the people who do it now wouldn't do it (this ignores truly non-profit crimes, but does include crimes that appear non-profit but which yield an effective profit by making other people be worse off). On the other hand, you can't go too far in the direction of exactly emulating our world in that respect, or the game will lose much of its lustre for many people other than the Goth crowd (which is what Vampire is for).