These may be failures to follow - but they are not in themselves renunciations of the principles to which you swore. A renunciation of your oath is and must be a more overt, deliberate and impactful thing, than failing to follow a tenet one time, or straying from the path you swore to. The oath and its tenets are different things: Failing, in a situation, to follow one of the tenets of your Oath is not the same thing as breaking your oath - they are very different things, by an order of magnitude.
Defining going against your word as the 'wickedness' spoken about in one of the tenets is also a stretch, and a very liberal one at that. Going against a word you give does not break any of the tenets listed, not on its own. What you are doing may end up in defiance of those tenets, depending on what it is, but simply breaking your word on something, without context of what, does not. More likely, in game terms, is that everything is keying off Oath of Devotion, since keeping your word is a devotion tenet, not an Ancients one... and others here have reported that failing to show mercy or preserve life haven't caused breaks.
If you're able, everyone should take a moment to set aside all internal thoughts and definition they might have of 'paladins must be good, honest, chivalric, religious, devout people' That is not a part of the definition of paladin any more, and has not been for the past fifteen years at least. Paladins can be anything - what matters is their dedication to particular ideals, divinities or causes, and the divine power they can tap through that dedication and faith. Nothing else is essential - not honesty, not integrity, not chastity (hah!), not eloquence, not fairness, not mercy, not forgiveness, not kindness, nor any virtue you care to name; none are essential to a paladin, unless their particular oath and cause
makes it so (such as Devotion, which
does make integrity an important tenet - but it's because of that specific oath, not because of paladin in general).
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I also have an issue with people claiming Paladins don't need gods and can be any alignments in 5e when the subclass talks using divine symbols and divine abilities all the time and the oaths tenets force you to act into specific alignment range.
It's not a claim; they don't. You might prefer the extremely old-school rigid lawful-stupid lock-in, but that's simply not the way it is; this is not a 'claim' - it's a fact, and has been so for the past
fifteen years of the game.
Paladins drawn on divine power to grant them capabilities, and it is the bond of their oath and their dedication to it that allows this. The power does not need to come from a specific deity, or any single deity at all, and the Paladin does not need to worship a particular deity, even if the source of their divine power is drawn from that deity's portfolio in some way. A holy symbol is a focus for your Oath - it
Can be the symbol of a deity who serves as your divine intermediary, if that's the route you take, but it doesn't need to be. It only needs to honestly represent the form of your Oath - an Oath of Glory Paladin might even use their own family crest as their symbol. In that case, their power most likely derives from tapping the folios of divinities who favour champions and heroes, or divinities who appreciate individual excellence of body and form - and many of those latter aren't nice divinities, by the way, and the Oath of Glory in no way requires you to be a good person, by any stretch. Importantly, though, the Paladin in question may not even know who any of those divinities are, and certainly does not need to worship them, or preach their name - simply doing the work that their oath entails is enough. The individual Oaths are quite varied as well - but how they are conducted leaves space for a broad spectrum of alignments (some more than others, granted). Between all the various oaths we have, there is room for a paladin of any alignment to comfortably exist. Remember: alignment is not so much about what you do - it's about why you're doing it. Everyone can be the person that saves the world, good or evil, lawful or chaotic - why they are saving the world, however, is another matter.
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