Why Couldn't The Jedi Sense That Palpatine Was A Sith Lord?

Three things stacked up. Palpatine was the single most accomplished user of Force concealment the galaxy has produced, and he hid his dark nature from the Jedi High Council for years while sitting in the same room as them. The Jedi Temple was built directly on top of an ancient Sith vergence whose dark energy the Order never fully neutralised. And a thousand years without a visible enemy had left the Jedi badly out of practice at hunting one. (Revenge of the Sith; Tarkin; The Phantom Menace)

They could sense something. Just not him.#

The Jedi Order were not blind. They sensed the presence of others and read feelings as a matter of routine, and by the late Clone Wars plenty of them knew something was badly wrong. The Council understood a plot to destroy the Order was in motion. They knew the dark side hung thick around the Chancellor's office. (Attack of the Clones; Revenge of the Sith)

None of that got them to the answer. Knowing the dark side surrounds a man is not the same as knowing the man is its source, and every Jedi who noticed the fog explained it as something happening near Palpatine rather than something coming out of him. That gap is exactly where Sidious lived. (Revenge of the Sith)

Buried Presence#

In the Legends continuity, the power at the centre of it is called Force stealth, also known as Force Concealment or Buried Presence. It allows a highly skilled Force user to mask their alignment, their sensitivity, or their entire presence from other Force users. (The Force Unleashed Campaign Guide)

Legends does not hedge about who was best at it: Darth Sidious, the most powerful and notorious user of the ability. The films show the result. He hid his dark nature from the Jedi High Council through his whole rise to power, up to and including while he was in the same room as them. This is a Sith Lord sitting in the Chancellor's chair, in a building crawling with the most sensitive people alive, with his signature turned off. (The Force Unleashed Campaign Guide; The Phantom Menace; Revenge of the Sith)

The technique was not unique to him. In Legends, a derivative called Quey'tek meditation let a Sith Lord or Dark Jedi mask their dark signature well enough to seem completely benevolent to even the most alert Jedi, and both Asajj Ventress and Darth Maul made use of it. Concealment is not an exotic trick. It is a known discipline, and the Sith had a thousand years to perfect it while nobody was looking. (The Cestus Deception; Darth Maul: Shadow Hunter)

The building they put it in#

The second problem is architectural. The Jedi Temple on Coruscant was not built on neutral ground. (Tarkin)

Underneath it sits the Shrine in the Depths, an ancient Sith shrine constructed at a Force vergence during a period when the Sith dominated the galaxy, dated to no later than roughly five millennia before the rise of the Empire. The Jedi built their Temple on top of it deliberately, hoping to neutralise the dark energies below and occasionally using the space to nullify dark side artifacts. In the Legends continuity the same idea appears as a wellspring of dark side power beneath the Temple. (Tarkin; The High Republic: Into the Dark; The New Jedi Order: Traitor)

The problem with capping a vergence is that capping is not the same as removing. The Jedi did not stop the power of the shrine. They built a school on it and told themselves the matter was closed. (Tarkin)

Sidious went further than they ever did. Once the Temple became the Imperial Palace, he had the shrine excavated by droids working under his personal protocol unit 11-4D, kept its existence so secret that even Vader did not know, and used it as a private sanctum where he spent much of his time meditating on the dark side. His long-term intention was to probe it for the dark side's deepest secrets and reshape reality to suit himself. (Tarkin)

A thousand years of being right#

The third reason is the one the Jedi did to themselves. The Order believed the Sith had been extinct for over a millennium, and it believed it hard. (The Phantom Menace)

That belief shaped everything. An institution that will not examine its enemy loses the ability to recognise it, and by the time of the Galactic Republic's final years the Jedi were simply not practised at seeking out the dark side. They could feel it. They could not read it. (The Phantom Menace; Revenge of the Sith)

Set that against what Darth Bane's Rule of Two was designed to do. Two Sith at a time, no armies, no visible order, generations of patient positioning while the galaxy assumes you are a myth. It is a strategy engineered specifically to exploit an enemy who has stopped looking, and Sidious inherited it fully formed. (The Phantom Menace; The Clone Wars, "Sacrifice")

Add complacency to arrogance and the outcome is close to inevitable. Mace Windu and the Council were the most capable Force users of their generation and they were also the least equipped generation in a thousand years to answer the question they were being asked. The Sith did not out-power them. The Sith out-waited them, hid in the one building the Jedi trusted most, and let the Order's own confidence do the rest. (Revenge of the Sith)