The ice cream is worse, because attempting to remain polite is far harder in this situation. It's like... well I don't want the rest now, but if I chuck it, they'll wonder what I'm doing. With the drink you can just put the cap on and chuck it later, or even offer them the rest with a polite 'I don't really want any more'. Doesn't work so well with an ice cream really... who gets half way through and doesnt want it? Precisely.
EVILS:
Someone asking for some of your chocolate bar whilst in a group (say the 50p dairy milk ones), you say yes to that ONE, and you end up giving all bar one square away to the rest
OR
Asking somone to buy you something specific at the store, waiting eagerly in anticipation and they've forgotten/got the complete wrong thing. (could you get me a Double Decker please - I got you a DM fruit and nut, for instance)