In both cases they're wrong. In the first instance, there's a debate to be had about the impact of imperialist pasts, but certainly neither I nor you (I'm a white person, and I am supposing you are too, but please correct me if not) are responsible for the world's ills. In the second instance, that's bullying, and the appropriate interventions should happen - school, parents, and other societal pressures.
But neither adds up to hate speech, because vulnerable groups in society are not being targeted for their vulnerability. We preserve special punishments for hate speech (at least in the UK), and they should only be applied to limit free speech in defence of those vulnerable groups.
Not to say those situations aren't wrong - they are. But where more vulnerable people are targeted, extra protections are appropriate.
Your understanding of the purpose and application of hate crime laws in the UK is wrong, since they make no distinction as to whether or not the group to whom the hate is directed is especially vulnerable. Hate crimes directed against dominant and majority groups are still hate crimes - one of the most famous convictions for incitement to racial hatred was that of Abu Hamza. Whilst some of his charges were specifically for incitement to murder Jews; he was also convicted of incitement to murder non-Muslims in general.
There was a prominent news story this year when someone spat in a baby's face and informed it's mother than 'white people shouldn't breed'. He was convicted of racially-aggravated assault. This was actually his third conviction for a hate crime specifically directed at white people.
These are not the only cases - just the two most prominent news stories I could think of. Outdated stats from 10 years ago show that half of the convictions for crimes motivated by racial hatred were perpetrated against white people. This does include 'white-on-white' hate (English against Polish, for example), but other cited cases included a white guy beat by Bangladeshis and a white Scottish man murdered by an Asian man.
You may be of the opinion that we should reserve the term 'hate crime' for crimes committed against vulnerable minority groups, but that's not how the law in the UK is written or applied.