I'll admit, a big part of my reason for that belief is narrative causality - I would not find this evidence convincing in an open world, but in the context of a fictional story, it fits a little too neatly for coincidence. It's obvious that Harry is going to move out of Dumbledore's camp at some point - their worldviews differ too strongly - but this would make an absolutely beautiful cause for the split.

And yes, "I don't give in to intimidation" is a good start for getting people to stop threatening you, but "...and if you try, I'll start intimidating your people and see how you like it" works much better. There's a reason nuclear deterrent involved having your own nukes, and not just saying "London can take it" writ large.