MORE SPOILERS AHEAD
Wolvie did it to help MJ out; to help her move from grief to anger. She was consumed with the grief of losing Peter. It was all she could focus on or think about, and it was destroying her little by little. Wolverine knew if he did what she did, she'd be furious with him and want to kill him. If she had to be obsessed with something, he'd rather she's obsessed with thoughts of killing him than the loss of Peter.
The shedded skin that Peter left behind was kind of cool though.
Quick Review
(From Memory)
MJ & May greiving.
Cap consoling May
Tony discussing with MJ on how he has was of making Pete's death look like an accident.
Jessica talks to MJ and says that she felt some kind of connection to Pete during his final moments, even though she wasn't there.
MJ giving in to grief.
Wolverine hitting on MJ.
MJ deciding to find a way to kill Wolvie.
Crash is heard in the lab where the body is being kept.
All run to area, and find that someone broke through lab window, skinned Pete's body, left the skin and escaped.
Closer exam shows that the window was broken out of, not in to.
Closer exam shows body wasn't skinned, but rather the skin was shed.
Boy on a fieldtrip with classmates sees a giant slimy cacoon under a bridge, but doesn't tell anyone for fear of being made fun of.
That's in in a very quick nutshell.