Jesus said the birds don't worry, but then some birds starve to death or get eaten. Shouldn't birds worry?

Read Matthew 6:25-34 and Jesus tells people not to worry about getting what they need to live, because birds and flowers get what they need. However, a lot of birds and flowers have untimely demises. If they could think better, wouldn't they worry, too? Also, why doesn't food fall from the sky for people who don't worry?