Strangely, it appears that the ACS moved or deleted the linked article, but we can still investigate the claim.
As far as I can tell, there are two main concerns about plastics in water bottles: the kind of plastic used and the size of particles it can break down into.
Though an article published by the NIH states that, on average, a liter of bottled water included about 240,000 tiny pieces of plastic, and that about 90% of these plastic fragments were nanoplastics (<1 μm in size), they noted that "the potential health effects of these tiny plastic bits are still unproven and unknown".
However, a particular plastic called bisphenol A (BPA) was identified in this article by the BBC as a potential concern, though it concludes that "At present, there is no strong, conclusive evidence that at the everyday concentrations we may be exposed to, BPA can cause harm." Statements by regulatory bodies like the FDA and EPA also support this.
This is countered by another study published by a group of researchers from the Manipal Academy of Higher Education in Karnataka, India that suggested that BPA exposure—even at low doses—is linked to serious health risks including hormonal disruption, increased risk of several cancers (like breast, prostate, and ovarian), interference with cancer treatment, and epigenetic changes that may promote tumor development.
In conclusion, the claim "drinking water from plastic bottles gives you cancer" is too broad to make and needs context. While it's true that BPA (a plastic linked to cancer risk at low doses) may be harmful, it is not used in all water bottles and is typically not found in disposable water bottles, which are usually made from PET (polyethylene terephthalate). Further, the FDA and EPA maintain that current exposure levels are below any level of concern.
