In Episode 3 Obi-Wan ignores Yoda:
Why would he not take Yoda's word that he would find pain if he looked at the security video?
I think that it's basically exactly as his dialogue indicates, he feels he "must know the truth" even if it does bring him pain. This fits in with what we know of his moral strength and willingness to bear pain, his inclination to not blindly conform to what it is told to him by his superiors (a trait no doubt nurtured by Qui Gonn), and his desire to understand.
First, he believes that he needs to know what happened (though he already seems to suspect it). From Revenge of the Sith:
OBI-WAN: Wait, Master. There is something I must know . . .
YODA: If into the security recordings you go, only pain will you find.
OBI-WAN: I must know the truth, Master.
Second, the novelization offers some additional insight into his motivation:
“Seeing will only cause you pain.”
“Then it is pain that I have earned. I won’t hide from it.” He keyed a code that brought up a holoscan of the Room of a Thousand Fountains. “I am not afraid.”
Revenge of the Sith
Obi-Wan seems to feel that he deserves whatever pain watching the video will bring him. He already suspects what it will show, and regrets his part in it. As Yoda says earlier:
Obi-Wan rose. “I will learn who did this.”
“Learn?”
Yoda shook his head sadly.
“Know already, you do,” he said, and hobbled off into the gloom.
Revenge of the Sith