He had two options. Phobe or Mo. Mo had a solid two allies in Jacqui & Tarzan. She knew that Dave worked well with Mat and he also tried to throw the challenge to save Mat. Mo trusted Mat and so she trusts Dave based on those two evidence. Phoebe didn’t vote with David to take out Nick so he lost her trust. Her other ally options were Lee/Sharn who are floaters. So Phoebe brought less to the table than Mo. He could sway Zach himself as they were bros. So Dave made the right move. He also wanted to own this vote out: if Phoebe had found the idol the control would go to her and her allies. By showing the idol, he shows he controlled this vote out. It wasn’t some random flash