The phrase "to support this statement" means providing evidence, reasons, or examples to show that what has been said or claimed is true or valid. Full definition
For example, if your critical essay writing is based on a book, you may argue that the main theme is love and support your statement with evidence from the studied book. (custom-essay.ws)
Not only that, I've found that research sometimes doesn't support the statements of the authors. (judithcurry.com)
Yes, it slows the process but the science does not support your statement that probiotic bacteria die after a few weeks. (thyroidpharmacist.com)