If Haytham was a Templar, then why does he have the marking of the Creed on his hand armor?

As the game reveals, Haytham was originally an Assassin. He eventually switched sides. But he maintained his Assassin skills over the years, as the first few hours of the game showed. Apparently, he obtained the gauntlet from Miko, another assassin.

Out of universe, it makes sense that the developers had that subtle sign on his clothing, as it would help fool perceptive gamers into thinking he was an Assassin, prior to the reveal. I don't recall there being an in-universe explanation for that though, it's possible it's just a part of the Assassin gauntlet, and Haytham didn't feel the need to customize it by removing the symbol. By the time that we the game starts, the Templars had largely killed off the local Assassin presence, so we never saw if Haytham used it to fool Assassins.

Desmond received an email from Shaun Hastings about that blade :

From: Shaun Hastings
To: D. Miles
Date/Time: Nov. 13th, 2012 12:18
Subject: Haytham's blades
I've been doing some digging on Haytham's blades. Still not 100% sure where they came from. My initial instinct was he started out as an Assassin - I believe his father was one, in fact. But it appears he was a Templar from pretty early on. Maybe he took them from someone. It's happened before. And they're quite handy. I'm surprised more Templars haven't put them to use. Pretty easy to build a pair if you know what you're doing...

I looked it up on the wiki, I was wondering as well. The wiki shows that this was explained in Assassin's Creed: Forsaken:

In 1753, Haytham was ordered to kidnap a young rebel named Lucio Albertine in Corsica, who was being protected by the Assassin Miko. On being ambushed by the Assassin, Haytham lost his treasured short sword, though the fight ended when Haytham pulled Miko into a crevasse, but was subsequently dragged in along with him.

Miko grabbed hold of a rope and Haytham's arm to prevent himself from falling into a steep drop, though Haytham loosened Miko's Hidden Blade from his arm and bit his hand, causing Miko to fall. While this did not finish off his adversary, upon Haytham's suggestion, Miko fled to fight another day.

Afterwards, having the Assassin's Hidden Blade to compensate for his lost sword, Haytham then brought Lucio to Birch so that the Templar Grand Master could blackmail Lucio's mother Monica into decoding the journal that Haytham had retrieved from Juan Vedomir.

Haytham Kenway is the son of Edward Kenway, a privateer-turned-pirate then assassin, a Caribbean assassin - The protagonist of Assassins Creed 4 : Black Flag.

Ok so , now , after 3 years from the release of AC III we have the full story . Edward James Kenway was a Pirate turned assassin , who was Haytham's dad , as we see in the last cutscene of AC IV : Black Flag . In an official AC book , it days that Edward died back in England after the events of AC IV . When he died , Haytham was still training to be an assassin ,but he never knew what he was training for . Edward wanted to Tell him that he will become an assassin that day . After His gater was killed , Haytham and Jeniffer were "adopted" by Reginald Birch , the leader of the Templars . As he fortunately found out that Haytham didn't know that His father was an assassin , he told him that he needed to become a Templar . Now , the events of AC Rogue are coming . By that time , Haytham found out what His father truly was , but he chose to be a templar instead . This is when we find out why Haytham has a hidden blade . In the first cutscene of the mission "Caress of Steel" we can see Haytham making an assassin gang Member Tell him and Shay where Hope is hiding . After he found out what he needed , naturally , as he always does , he stabbed the guard in the neck . Shay asked him why does he have a hidden blade and Haytham says it was "donated" by the Brotherhood ... So he actually killed a random assassin and stole his blade . He was never an actual assassin and he didn't use His blade to make the assassins think that he is one of them . He used it to slaughter . Hope i helped . Bye !

If you see Haytham's interaction in Rogue with Shay when interrogating a guard

Shay looks at Haytham seemingly surprised

Haytham: "What? You thought you were the only with hidden blades?"

Shay then asks how he got them and Haytham replies, that it was a "donation" from the brotherhood.

Haytham Kenway was never an Assassin. His father, Master Assassin Edward Kenway, had begun to instruct him in sword fighting and the basic philosophies of the Assassin Order when Haytham was a child. However, before he could tell Haytham why he was being trained, Edward was murdered by mercenaries hired by Reginald Birch, a business associate of Edward. Birch, unbeknownst to Edward, was the Grand Master of the British Rite of the Templar Order. Haytham's sister, Jennifer, was kidnapped and Birch secretly had her sold to slavers. After that, Haytham studied under Birch as a Templar.

Many years later, Haytham had been tasked with retrieving a boy names Lucio, whom was being guarded by an Assassin name Miko. Haytham managed to kidnap Lucio, but ran into Miko shortly after while descending a cliff. Needless to say, a fight ensued, during which Haytham's short sword was lost. Haytham managed to knock Miko off the ledge, but Miko grabbed onto his arm. Haytham proceeded to remove Miko's hidden blade in an attempt to get him to lose his grip, which he succeeded in doing. Miko survived the fall by grabbing onto the rope Haytham had been using to climb down the cliff. Haytham gave Miko the choice of falling to his death, as he was poised to cut the rope, or leaving and living to fight another day. Miko decided on the latter option, and Haytham kept his hidden blade as a replacement for his sword.

Also, just to key you in on the irony of the situation, the first person Haytham killed with that hidden blade was it's former owner, Miko (The man in the theatre box in the opening sequence of AC III).

When Haytham was young, he saw a templar killing an assassin and then leaving the body; that was his first time to loot a body.

That's what I think happened.

When Haytham fought against another assassin,Miko, on a mountain,he was about to push Miko off the mountain.However,when he saw the hidden blade on Miko’s arm,Haytham removed it and pushed Miko to his death.

The hidden blade with the Assassin Symbol on it was a stolen blade from Miko (the man Haytham kills at the beginning) to supposedly replace his own broken sword (since the novel by Oliver Bowden is his own ideas on the AC characters, it's hard to know how much of it is canon), where the other blade (he has two) came from is a mystery.

Haytham was being trained to become an assassin from an early age by his father, Edward (AC4 Black Flag's protagonist), much like Federico was by his father, Giovanni, in AC2. Much like Federico and Ezio too, Haytham didn't know why or of his heritage or the Templars being enemies etc. only his daughter, Jennifer, knew what her father's true vocation was, so his mother wasn't privy to this either.

When Edward discovered that Reginald Birch was a Templar (his daughter told him) he argued with him and told him to get out, however Haytham had inadvertently told him about his father's secret safe in the library as that was where he had put his son's future sword and he was after the journal documenting first civ stuff etc. He got Braddock's thugs (in disguise of course, hiding the Templar symbol on them) to break in to try to retrieve it where a fight broke out which ended up in Edward's death and Jenny was kidnapped and sold into prostitution. Haytham defended his mother to save her from the same fate as Maria Auditore (rape or sexual assault) by the thugs by stabbing one of them in the eye, killing him instantly, and she stopped loving him for it forever - she handed him over to Birch and she died years later having never forgiven her son.

He was thus indoctrinated into the Templar order by Birch (from the age of 10) and didn't find out until later having found Jenny that he had been lied to and Birch had been responsible for his father's death and his mother's disowning of him too, though why he would remain a Templar is beyond me. Although in AC: Unity we find out he wrote letters to his sister (who was in contact with Elise and her father who have so far been the only nice Templars in the series) saying he wanted to unite the Templar order with the Assassin order (perhaps after meeting his only son, Connor maybe). Pity both Charles Lee and Achilles got in the way of his relationship with his son, Achilles just wanted revenge for Haytham crippling him and used Connor to do that, and Charles had become a corrupt power hungry drunk and wanted Connor dead and not just because he was an Assassin but because he thought he was too much of a distraction for Haytham and wanted Haytham to kill him - which he didn't do because he was his son and loved him (that piece of crap, Otso Berg said Haytham was weak for loving his son and should have killed him regardless). So Charles manipulated Connor's childhood friend instead, which unfortunately backfired and made Connor want Lee dead even more. It is a shame that life for Haytham had been so different to what it should have been, Edward would have never wanted this for Haytham although I do think he should have been less clandestine with his family especially his wife and son with regards to his heritage - sad really.

PS: It is the Animus that fools the player (and Ubisoft, of course) into thinking Haytham is an Assassin not Haytham himself.