Initially because Poe Dameron has just been demoted from commander to captain for his hotheadedness; he's no longer in the top ranks. It's likely that Admiral Holdo is also trying to teach him a leadership lesson, citing Leia Organa's comment about hope being like the sun; just because you cannot see it at night (the darkest time) doesn't mean it isn't there.
There's also a clash of leadership styles, as director Rian Johnson explained who he set up the conflict between Poe and Holdo in this L.A. Times interview:
“[Poe] is a hotshot pilot, so you ground his X-wing and you face him
with the question of bravado vs. true heroism, which is leadership. I
started watching World War II movies, because you see that type of
relationship reflected a lot in films like ’Twelve O’Clock High’ or
‘The Dawn Patrol.’ The fact that it’s a woman, and not only that, but
it’s a woman who isn’t in a general’s outfit but has a real feminine
energy, seemed like the toughest thing that Poe could come up
This conflict heats up just as it appears that Poe has a chance to learn about the main plans: As he enters the command room, he sees that the shuttles are being fueled and he loses his temper. He accuses Admiral Holdo in front of the rest of the remaining command staff of being a coward and a traitor. Since a military commander cannot tolerate insubordination, Poe is ejected from the command area. (Note that this also follows his refusal at the start of the evacuation to follow Gen. Organa's orders to abandon the attack with the bombers.)
Thematically, Poe's failure to have hope in Holdo, along with the insurrection and the failure of Poe's alternate plan for escaping from the First Order sets him up for future leadership of the Resistance, at least in terms of Yoda's speech to Luke: "Failure is the greatest teacher."