Two kinds of plaintiff
Competitors usually sue under the federal Lanham Act, which lets a business harmed in its sales or commercial reputation challenge a rival's false or misleading statements about goods or services. Consumers generally cannot use that statute. They tend to rely on state consumer protection law instead, and in New York the General Business Law provisions on deceptive practices and false advertising are the usual vehicle, often in a proposed class action. The Federal Trade Commission and state attorneys general also police advertising, although the FTC Act itself does not give private parties a right to sue. Which kind of case you face shapes what has to be proven and what is at stake.
False on its face, or misleading in context
Courts commonly separate claims that are literally false from claims that are technically accurate but leave a misleading impression. A statement that is false on its face is usually easier to challenge. A misleading claim often requires evidence of how buyers actually understood it, and consumer surveys become a frequent battleground. Comparative claims, claims that testing proves something, and labels like "natural" draw a large share of disputes. General boasting that no reasonable buyer would take as a measurable fact, often called puffery, is usually not actionable, although where puffery ends is argued case by case.
Opening moves on each side
If you are challenging an ad, we look at what substantiation the advertiser is likely to have, what evidence of harm to your sales exists, and whether the advertising self-regulatory process run by BBB National Programs would move faster than a court. If your advertising is the target, we start with the substantiation file: the testing, studies, or data that existed when the claim first ran. Preserve the drafts, approvals, and test results behind the campaign. Changing a challenged claim can be a sensible step, but do it deliberately and keep the earlier versions. Delay matters in both directions, because a request for an injunction loses force when the party seeking it has waited.