it all comes down to frequency. if you get upsetting news less than once a month [in other words, this lack of hunger is a one off thing], skipping a day of eating isn't going to hurt you unless you have some other medical condition going on. your body is designed to be able to have a stomach bug here and there and one day of not eating isn't going to hurt you long term, so long as it's really one day. now, if it's always something [upsetting news, too busy, any number of other things] making you not eat, that's when it becomes an issue. and that's the point where you need to be making yourself eat.
one day of not eating due to upset isn't starving yourself. if it's still a problem tomorrow or the next day, then you need to make yourself eat. but unless your "upsetting" is a life altering void that you're being thrown into and you're not sure how you're ever going to function again [in which case by all means start force feeding yourself to get used to it], you'll probably be somewhat back to normal tomorrow plus be a little hungrier to make up for not eating today. your body is really well designed to balance out those sorts of little ripples.
if it is the big sort of thing that's going to be a long time working through, then the blandest and snackiest things are the easiest to eat. when there isn't so much a food aftertaste it's easier to pop in another bite in and chew. think nuts and crackers to eat and juice or ensure to drink.
-google first. ask questions later.