What if they're bullied? Molested? Abused? Are they not entitled to their feelings?
If you always believe you're not allowed to feel bad because someone's worse off than you it's just as difficult to deal with life as if you wouldn't allow yourself to be happy because someone is richer or more successful than you. If you hear a person, child or otherwise, complaining about their problems who does it actually help to point out that there are people out there starving? Do you automatically assume that person has severely sadistic tendencies and gets some sick enjoyment out of the idea of other people suffering? Or are you just trying to belittle their issues to get away from the conversation?
You wouldn't walk up to a recently orphaned starving child and tell it:
"Don't complain, there are orphans in other countries starving and on top of that they have HIV and they're missing limbs after stepping on landmines."
Or at least I hope no one who reads this would do that...or anyone at all for that matter.
To quote the emotional masterpiece Team America: "Maybe feelings are feelings because we can't control them." Don't control your emotions, don't let them control you but work with them, deal with them and you'll lead a happier life.