The other toys drove Woody to jealousy
When Buzz first arrived, Woody was the reassuring one, letting all the toys know that they wouldn't ever be replaced and despite potential new toys they would always stick together, yet the behaviour of some of them (notably Hamm and Potato Head) were almost taunting Woody.
For example when Buzz is showing off his buttons and gadgets, Hamm and Potato Head didn't just admire them, they made a point of expressing the major difference between Buzz's buttons and Woody's string. Even Bo Peep chipped in with "I've found my moving buddy", which was a heartless thing to say, and to then wonder why Woody was feeling insecure.
They were all worried that a new toy from Andy's birthday would replace them and their role within the gang and it was Woody who assured them that wouldn't happen, yet as soon as Woody is on the verge of replacement, the toys providing no support whatsoever and pretty much cast him aside.
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