Why didn't Dumbledore ever teach or suggest the usage Legilimency to the members of the Order of the Phoenix, for investigative purposes as well as an advantage against the Death Eaters during duels? Surely, he would have thought of it, as in the Half-Blood Prince, the summary of the book says that the war against Voldemort and his army (Death Eaters and creatures) was not going well, and that the Order has already suffered losses (such as Sirius Black, a skilled duelist who held his own against Dolohov and Bellatrix, the most powerful Death Eater). Why didn't Dumbledore teach Legilimency to the Order of the Phoenix members as well as the Golden Trio (Harry Potter, Ron Weasley, Hermione Granger) when they were constantly battling Death Eaters and trying to find out more info on how to beat them and needed all the advantages against them?
An example would be Borgin and Burkes. We see in the Half-Blood Prince film, I don't know about the novel, that Death Eaters entered their shop. Arthur Weasley sent an agent there, as he told Harry during the Christmas and New Year Holidays. If the agent performed Legilimency, the agent may have learned not only of the purpose of why Draco wanted to mend the Vanishing Cabinet, but also possibly where the Vanishing Cabinet in Borgin and Burkes leads to (Hogwarts Room of Requirement). This would have allowed Dumbledore, via their relationship in the Order of the Phoenix, to shut off, via a destructive spell like Bombarda or Incendio, the Hogwarts Room of Requirement Vanishing Cabinet, and prevent the break-in that caused the Battle of the Astronomy Tower.