I get so sad when people build Eve wrong.
She is 111% AD assassin. It isn't even an argument, really.
Can anybody please explain their rationale of insisting to build her AP or tanky?

She is 111% AD assassin. It isn't even an argument, really.
Can anybody please explain their rationale of insisting to build her AP or tanky?

She has dual scaling on all her spells, how is she "111% ad?". She was originally designed to be a hybrid
Honestly her build is really versatile, but AP build offers good DPS on top of strong burst with R and E and access to runic echoes and lich bane for movespeed. The AP build also kites better and isn't as shut down by cc or slows. You also get access to rylais and hourglass which give amazing utility. Furthermore, the AP build supports an assassin playstyle more as you don't have to spend as much time in the brawl to get your target. An AP build can usually get away with less defense and thus more damage because of this.
ap - because everything scales with ap( ult doesn't even have ad scaling) and you can get more ap than ad, doesn't have to auto attack to deal damage( ad doesn't need to either but unless you're auto attacking you deal less damage than ap, if you are then ad does more damage).
tank - she does a lot of damage and being a tank means she can stay in the front line without dieing while still being a threat. Plus bruiser/tank items are strong these days. 
also
is a perma-slow
eve's made so that she can have multiple build paths. whether it's ad, ap, or tank
Ap assassin or ad assassin or bruiser or hybrid or tank. They can and do all work on Eve depending on what your against.
i can''t speak for people who play tank eve... But in terms of AP vs AD... eve really relies on her early game a lot, so getting runic echos on her gives her movement speed and burst on her q and e, so with just one item she can be insanely powerful along with the benefits of rylies and you can use nashers tooth more efficiently, along with gun blade.
I've always seen eve as a Hybrid assassin instead of either pure AD or AP.
undoubtedly AD can deal much more damage in less time, due to BOKR cleaver devouerer etc. but she requires much more time to get herself set up with the needed items.
so in a game of squishes that should be a shorter game i usually build AP and go for early ganks and assassinations, but for longer games with multiple tanks i spec for devouerer, with BORK, cleaver, rageblade, and deaths dance.
She is not the easiest jungle to master. I have tried that before.
Because she has no dashes or range and very weak burst, even when building glass cannon. She will die before she kills anything.
AP Eve generally benefits from more utility items, a much quicker power spike, stronger ganks, and stronger burst. AD benefits from the current meta, has more lategame potential/sustained damage, and clears more easily. Tanky bruiser benefits from pretty high utility, high early pressure, and being a massive annoyance. Very much depends on what you want to accomplish with her for which build you might go for.
That being said, I've always been very leery of the glass cannon AD build for Eve (Triforce, BT, Maw, and Mercurial do not leave her durable enough). She suffers badly from an inability to get away once she commits and initiating with her is pretty stupid unless you're running the tanky bruiser version. Against a team with some reasonable coordination, not only are you going to have difficulty snowballing enough to afford the pretty expensive build you prefer, but you're generally going to get focused and CC'd/bursted down before you can take down your target. Regardless, if it works for you go ahead and keep using it. Just describing my personal experiences with the champion and the style of play.
So one of the most sad things is when people say that my build has no burst.
If I had a dollar for every time I had an opponent mention "that damage" after blowing them up before my E buff was off, I would have all the skinz.
I just can't for the life of me understand why, with a 120% AS buff, someone wouldn't utilize that insane potential. Fervor of Battle is incredibly easy to get full stacks on, Challenging smite, and exhaust, and I name someone I can't duel. Which makes her a split push a nightmare to deal with. You can just eat anybody and if you are stealthy enough you have the tools to get in, get a kill, and get out very fast, very often before the enemy even has a chance to react.
I have been maining Eve since she was considered the worst champ in the game and was very difficult to get a ranked game with without being harassed extensively and a dodge. I'm incredibly familiar with her.
They build her tanky because EVERYBODY IS GOING TANKY Everybody.
Tanky builds are the in-thing currently in the current meta because there aren't enough strong anti-tank setups that don't include "Have vayne" or "Have kogmaw" or "Have your own tanks".
I personally think Evelynn is one of those relics from a long age ago who's currently an utter mess in terms of damage and build paths. She desperately needs an overhaul so she can get up to speed and pick either AD or AP as her poisons of choice. Hybrid champions are awkward to build around and not particularly efficient.
My last game, FOR EXAMPLE, I had 417 AD, Full AS with E, 40% lifesteal, a Sated Devo around 16 minutes and a TriForce.
Can AP Eve solo baron or almost 1v5 an entire team? I don't think so.