Why was Luffy never offered a Shichibukai position? I recall that a shichibukai needs to have quite a good bounty, and be very strong. So why was Luffy never offered the position? I mean his second bounty was higher than Crocodile and Hancock, so if we say he offended the World Government in the Enies Lobby arc, then before that, he was eligible, and even afterwards, we can't say he's not eligible; let's not forget Doflamingo threatened tenrybito with revealing some information, and his status was not revoked.

So why not?
First time around when Luffy took down Croc, BB offered to take the position of Shichibukai by presenting the marines with Ace. It was an offer the Marines could not pass up on, so they did not think of any other suitable candidates.

Also, since the credit for taking down Croc was given to Smoker, Luffy was relatively unknown. This further emphasized the reason as to why he was not considered because Shichibukais would generally be selected from feared and notorious pirates.

After the war of best, there were three vacant positions for the Shichibukai. But none of them were offered to Luffy. This is because Luffy by then has declared war against them by burning the flag of WG. He attacked Ennis Lobby, Impel Down and Marineford the three symbols of the Marines, he punched a Celestial Dragon and he rung the Ox bell 16 times which declared the coming of a new age of pirates. All this made Luffy as someone who would be an enemy to the world government not some random pirate like the other Shichibukais who were even though notorious pirates did not directly meddle with the affairs of the World Government.

This is the reason he was not offered the position.

Also considering Luffy, like Ace he would have never accepted that position because that would limit his freedom.