This article addresses a critique of "Cotton Gravity" (CG) by Clement and Noiucer, who argue that CG is not predictive due to an excessive number of spherically symmetric vacuum solutions and geometric constraints on the Cotton tensor. The authors refute these claims, showing that the critique misrepresents CG and fails to account for the theory's alternative formulation in terms of a Codazzi tensor. The field equations of CG, originally derived by Harada, involve a third-order tensor $ T_{abc} $, which is problematic due to ambiguities and non-universal applicability as a matter-energy source. However, an alternative formulation using a Codazzi tensor provides a more robust and consistent framework. This formulation avoids the issues associated with the Cotton tensor, such as the inability to handle non-vacuum conformally flat spacetimes and the ambiguity in defining vacuum solutions. The authors demonstrate that the claim of an infinite number of vacuum solutions in CG is incorrect. They show that the condition $ T_{abc} = 0 $ does not necessarily imply $ T_{ab} = 0 $, and that the Codazzi formulation allows for a more controlled and consistent treatment of the energy-momentum tensor. This formulation also enables the derivation of solutions that generalize known General Relativity (GR) solutions, fulfilling the Correspondence Principle. In the case of the Bianchi I vacuum, the authors show that the geometric constraint $ g^{bc}C_{abc} = 0 $ does not restrict the solution space, and that the Codazzi formulation provides a consistent and well-defined framework for CG. The critique by Clement and Noiucer is shown to be based on an exclusive use of the Cotton formulation, which leads to misunderstandings and errors. For FLRW models, the authors argue that the Cotton formulation leads to inconsistencies, while the Codazzi formulation provides a consistent way to examine these models. The Codazzi formulation also allows for the inclusion of effective energy-momentum tensors, enabling the study of alternative gravity theories such as Mimetic gravity. The authors conclude that the Codazzi formulation of CG is more suitable for addressing the concerns raised by Clement and Noiucer. They emphasize that CG is not without limitations, but it should not be dismissed. The theory has the potential to provide new insights into gravity and cosmology, and further research is needed to fully understand its implications.This article addresses a critique of "Cotton Gravity" (CG) by Clement and Noiucer, who argue that CG is not predictive due to an excessive number of spherically symmetric vacuum solutions and geometric constraints on the Cotton tensor. The authors refute these claims, showing that the critique misrepresents CG and fails to account for the theory's alternative formulation in terms of a Codazzi tensor. The field equations of CG, originally derived by Harada, involve a third-order tensor $ T_{abc} $, which is problematic due to ambiguities and non-universal applicability as a matter-energy source. However, an alternative formulation using a Codazzi tensor provides a more robust and consistent framework. This formulation avoids the issues associated with the Cotton tensor, such as the inability to handle non-vacuum conformally flat spacetimes and the ambiguity in defining vacuum solutions. The authors demonstrate that the claim of an infinite number of vacuum solutions in CG is incorrect. They show that the condition $ T_{abc} = 0 $ does not necessarily imply $ T_{ab} = 0 $, and that the Codazzi formulation allows for a more controlled and consistent treatment of the energy-momentum tensor. This formulation also enables the derivation of solutions that generalize known General Relativity (GR) solutions, fulfilling the Correspondence Principle. In the case of the Bianchi I vacuum, the authors show that the geometric constraint $ g^{bc}C_{abc} = 0 $ does not restrict the solution space, and that the Codazzi formulation provides a consistent and well-defined framework for CG. The critique by Clement and Noiucer is shown to be based on an exclusive use of the Cotton formulation, which leads to misunderstandings and errors. For FLRW models, the authors argue that the Cotton formulation leads to inconsistencies, while the Codazzi formulation provides a consistent way to examine these models. The Codazzi formulation also allows for the inclusion of effective energy-momentum tensors, enabling the study of alternative gravity theories such as Mimetic gravity. The authors conclude that the Codazzi formulation of CG is more suitable for addressing the concerns raised by Clement and Noiucer. They emphasize that CG is not without limitations, but it should not be dismissed. The theory has the potential to provide new insights into gravity and cosmology, and further research is needed to fully understand its implications.