How do you describe this trait/behaviour?

Solution 1:

Besides the great words @coleopterist suggested, that person can also be considered a "nonconformist", "individualist", or slightly derogatory "lone wolf", "loner" or "rebel"

Solution 2:

Such a person is not being a team player and is something of a spoilsport.

Definition of spoilsport
noun
a person who behaves in a way that spoils others' pleasure, especially by not joining in an activity:
‘Don’t be a spoilsport, Sidney.’

Similar terms: wet blanket, killjoy, party pooper.