Niba: If you hated broccoli as a kid, get ready for some sweet revenge.
Broccoli and many plants related to it all have sulfur-containing molecules. And these type of molecules have a delightful smell... they're present in things like rotten eggs, farts... you see, delightful. So when that compound gets broken down by the microorganisms that live in your mouth, sulfur-y smells are unleashed. So, of course you don't like broccoli!
And depending on your microbiome you could have more or less of these microorganisms in your mouth. So the smell is worse for some people than for others. 
But things could get better as you get older. Your microbiome changes over time because you get exposed to new microorganisms through sickness, medicine, food, and life experiences. So your caregivers who loved broccoli might just have different microbiomes from you.