He's saying that if you have money deposited in his bank, he has the right to take some of it because he has the right to a profit. And he believes (rightfully so in your case, apparently) that we would totally understand and be ok with that.
Most of us see that for what it really is, a blatant and VERY much undeserved cash grab. So blatant that many people are understandably wanting to take their money out of BofA, and are being very public about it.
Yes, clearly it's all about getting their grubby little hands in your cookie jar, that's completely the extent of the situation. You act as though he's saying he owns some of your money just because you bank with them. He's not going to keep withdrawing $5 if you leave the bank, they don't own what's in your account.
And having a right to something doesn't mean everyone has to accept it/understand it, because you in turn have the right to react however you see fit.
It's got nothing to do with him taking the money you have in their bank. It's simply an organization in search new ways to create revenue when one of their most significant income sources has been slashed so arbitrarily and severely by powers completely beyond their control. They can charge whatever fees they want, and you as a customer can react however you want. Just like every other business on earth, and I don't understand why everyone gets so up in arms when a bank behaves like a business.
Turn it around, if they don't have a right to make a profit, do they have no right to make a profit then? Or if you really insist, if they only have the right to 'try' to make a profit, isn't creating a fee still well within the bounds of "trying" to make a profit? It's not like they're taking it just for giggles.