For you that might be a confident definition, for others it might not mean "anti-constitutional" but "against the declaration of independence", for even others it might not create any clear association at all.
That's because something being "American"/"anti-American" is not sufficiently defined in this context. It triggers a highly subjective assumption of what it means, allowing people to evoke "us vs. them" solidarity without actually taking a position.
Example: I can (probably) break your assumed association by stating "women owning credit-cards is anti-American". It (probably) doesn't fit your mental model of what being "anti-American" means, but women were in fact not allowed to own credit cards in US until 1974. So my definition might be more in-line with the era of the constitution than yours.
That's a blunt example. Now imagine I use "anti-American" in a context of "law and order" and then keep talking. People instinctively glance over it because they create the meaning by taking their personal association of being "American" and invert it. You may feel like agreeing but I might actually say the complete opposite of what you think.
That's why IMO the phrase should be rejected from people in a public role.